Is relativity really relative? Because of the relativity of linear motion, you can't tell the difference between whether your spaceship is moving and the stars are standing still or whether you're still and the stars are moving the opposite direction.
But we know that I had to burn fuel to get my spaceship to move. We know that there's no amount of fuel that could get all the stars to move in the opposite direction. Therefore, the moving reference frame is my spaceship, because of energy constraints. So by considering energy constraints I was able to determine which reference frame was the moving one.
EDIT: So far only Dale understood my question.
 A: Cryo is right, and here is a good way to think about this. The Principle of Relativity says that, wherever I happen to be, all inertial frames are of equal status when it comes to writing down equations of motion and more generally studying physical effects. However, if the location where I happen to be is my own house, then the material structure of my house gives to me a natural choice of inertial frame that I may well prefer to all the others. This does not break the Principle of Relativity, which is a statement that no experiment within the house can tell me whether or not the house is in motion relative to some other frame such as the rest frame of the moon or a passing cloud or whatever.
Now the wider universe, at the largest scale, can serve as a house. The distant stars are where they are. Owing to the simplicity of their average motion on the largest scale (namely, the cosmological expansion which is uniform to a very high degree of precision), they present a natural choice of reference frame that I can pick if I want. What this is saying is that once you place yourself in the actual physical universe, it is perfectly possible to talk about a preferred reference frame. In cosmology it is called "comoving coordinates". If your spaceship is moving relative to comoving coordinates, at a velocity different from the one of the planet where it started out, then you can indeed deduce that its engines have been fired at some stage.
By looking at the cosmic microwave background radiation, the velocity of planet Earth relative to the comoving coordinate reference frame has been determined to pretty high precision. We can say that "Earth is travelling towards X at Y miles per hour". One might say that in some sense this feels like an "absolute" velocity, but in the technical sense of the terms "relative" and "absoluate" it is not; it is a velocity relative to something else, namely the average large-scale distribution of matter in the universe.
A: You need to be very careful in understanding what the principle of relativity claims. It claims that the laws of physics have the same form in all inertial reference frames. 
The reference frame of the spaceship in your question is not an inertial reference frame. Therefore the principle of relativity does not make any claim that it is equivalent to inertial frames. You are completely correct to note that it is distinguishable, but you are incorrect to think that this is in any way a contradiction with the principle of relativity. 
A: You seem to be saing that if there existed some preferred 'universal' rest frame then you could measure your speed relative to it, provided you could observe the necessary signals. 
A  candidate for such universal rest frame, I thought, could be the CMB rest frame. On this topic see Is the CMB rest frame special? Where does it come from?
But in any case. I think the point is that special relativity is a coherent theory that predicts observable and verifyable results, so existence of some universally observable rest frame does not invalidate it - the physics is still such that all physical laws are the same in all inertial reference frames. This is an emprical observation that remains unchallenged
A: 
An inertial frame of reference in classical physics and special relativity is a frame of reference in which a body with zero net force acting upon it is not accelerating; that is, such a body is at rest or it is moving at a constant speed in a straight line.

Italics mine.
You say:

Because of the relativity of linear motion, you can't tell the difference between whether your spaceship is moving and the stars are standing still or whether you're still and the stars are moving the opposite direction.

If there are no forces acting on the spaceship, it is just coasting in a straight line. If it is a satellite around the earth it is not in an inertial frame, as there is radial acceleration.
then you say:

by considering energy constraints I was able to determine which reference frame was the moving one.

"Know"means  a time recording and a measurement of the dp/dt from an inertial frame at rest to an inertial frame in motion versus another inertial frame. That is the way we do physics, we record, use the data to predict new frameworks. BUT between two inertial frames if there is no recording of how the energy to reach the spaceship motion was provided, there would be no way to know whether it is the universe that moves, or the spaceship. 
One needs to record in time, so a dp/dt can appear. There would be no possibility of knowing the expansion of the universe, if it were not recorded by nature in the doppler shifts of the spectra, a natural record.
A: By assuming that energy is expended in space travel you are implicitly assuming that the spaceship is accelerating. This is just Newton's law. This frame is no longer inertial. Thus you are comparing an accelerated frame to an inertial frame. However nothing in principle of relativity stops you from differentiating an accelerated frame from an inertial frame. 
On the other hand if you talk about a uniformly moving space ship then it is perfectly alright to see either one of them as 'moving'. 
$\underline{Note -}$
Incidently the answer to your question is exactly what resolves Twin paradox. Let the twins be T1,T2.
$\textbf{Setup}$ - T1 has started moving in a spaceship on Jan 1,2018 while T2 stays back at earth. They have decided that they will meet again in 50 years(taking into account time dilation and all that). So, when they meet who will be younger?
$\textit{We know moving guy should age slowly and hence stay younger}$ 
$\textbf{Paradox}$ - By relativity both frames are moving and hence when they meet both should see the other as younger. Hence a paradox! The setup is symmetrical or is it?!
$\textit{Who is actually younger?}$
If you think carefully you will immediately notice that just like your question T1 had to first accelerate to reach a uniform velocity. So the set-up is not symmetrical. Again to compare their ages they have to meet and reach same frame again. For this to happen the spaceshi guy has to turn around(again acceleration,non-inertial) and in the decelerate(again non-inertial). 
Thus we can confidently say that T1 is in non-inertial frame while T2 is in inertial frame. But we can apply theory of Special relativity only to inertial frames. Hence we are FORCED to work in T2's frame and conclude that it is T1 who should be actually younger.
This dramatic experiment has been done using particles called $muons$ and experimental results fit beautifully with the theoretical predictions. 
$\large \textit{Hail, O Einstein!!}$
