How is it possible photons have no mass but have energy? I know my question is so simple to ask but I'm new in this subject.
I'm studying energy systems engineering in university and I took physics and advanced physics but I never truly understand how photons have no mass but they're carrying energy. How is it possible ? 
I thought photons are some kind of pure energy but I saw NASA made solar sails to create propulsion, how can you create propulsion without exhaust mass ? (Momentum equation collisions) 
Also how can we "create" photons ? Like you can convert something into something else but creating must be impossible. 
I read about double slit experiment and it confused me even more and  it gets more and more complicated the deeper I go. 
I'm sorry if my lack of knowledge or English making my question hard to understand & read 
 A: It's a matter of classical mechanics & relativistic mechanics.
In classical mechanics, momentum ($p$) is proportional to the mass and the velocity of an object ($p=mv$)  and kinetic energy is $E_k=\frac{1}{2}mv^2 $. Thus you might think photon has no momentum and energy since mass is zero.
However, according to the relativistic theory, all these formula is changed. The mass of an object with certain velocity is increased by a factor of $\frac{1}{\sqrt{1-\frac{v^2}{c^2 }}}$. Since the velocity of speed of just what we call 'speed of light' ($c$), this factor becomes infinity and we can guess the momentum of photon might be a finite quantitiy. $(0\times\infty$)
More precisely, what Einstein found is $E^2 =m_0^2 c^4 +p^2 c^2 $ where $E$ is the energy, $m_0$ is rest mass, $p$ is momentum.
$m_0$ of photon is $0$, so $E=pc$ for photon. Energy of photon is $E=h\nu$ where $h$ is planck constant and $\nu$ is the frequency of photon. Automatically the momentum of photon is $p=E/c=h\nu/c$.
A: It all started with Einstein photoelectric effect explanation. If you have light of frequency v, you can receive energy nhv, where n is integer. There comes the concepts of photon in which we say light composed of particles called photons of energy hv, thats why we can receive energy nhv from light where n is always integer. We can say photons are Quantum of electromagnetic energy. 
       Photons always travels with speed of light. Rest mass is zero means it cannot exist at rest. We should not talk about mass of the photons. Only its energy and momentum are well defined. (Compton effect confirms photon have momentum). 
Two kind of things can happen with photons. If an atom makes transition from higher energy to lower energy, in the process, atoms energy will be decreased and photon will be created (emitted). An atom from lower energy state, can 'absorb' photon and go to higher energy. In that process, photon will vanish, we say atom absorbed it.
We can use probabilistic interpretations to explain double slit experiment with particles. 
So, even if we treat light as photons, we can explain double slit experiment.
I tried this in these videos: At the end of this video: https://youtu.be/I77WbGqKM4U
At 31:00 in : https://youtu.be/fpEg9a-YsXU
