Combustion Chamber Pressure I am going to calculate thrust for a theoretical solid propellant rocket engine I will be making. I have come across many equations for all sorts of aspects of the rocket engine. 
The measurements I have available are the dimensions of the combustion chamber, thrust needed by the engine after everything is done, and combustion chamber temperature. 
Thrust is defined as:
$F={\dot {m}}*Ve+(Pe-Po)*Ae$
Where 
               ${\dot {m}}$= mass flow rate
               Ve = exit velocity
               Pe = exit pressure
               Pa = ambient pressure
               Ae = exit area
Pe is very important because in order to get the highest thrust and avoid underexpansion it needs to be equal to ambient pressure. I need to find Pe and it is found by taking the throat pressure. Now I can't even being the exit pressure equation because I need throat pressure. Pressure at the throat is defined as:
$Pt=Pc (1 + (k-1)/2)^-k/(k-1)$
Is there an equation I could use to find the combustion chamber pressure so I can calculate throat pressure, exit pressure, and eventually nozzle dimensions?
 A: The thrust is maximized when the momentum flux is maximized.The Mach number at the throat of the nozzle is 1. 
The other constraint you have is that the exit pressure, $P_e$, is known and set to your ambient conditions. 
The missing fact is that once the flow is choked, it is not possible for further changes in the ambient pressure to affect the mass flow rate and therefore the upstream pressure is unaffected. If you go through the equations and examples for an isentropic nozzle, you will find that for air (where $\gamma = 1.4$), the critical value for throat pressure and choked flow is:
$$P^\ast = 0.5283 P_0$$
where $P_0$ is the stagnation pressure in the chamber. 
If you know the chamber pressure and need to find the throat pressure you reverse the equation:
$$ P_0 = \frac{P^\ast}{0.5283} $$
and that gives you the stagnation pressure required in your chamber. For your actual motor, with actual heat release and propellants, this will not be the same equation and you'll have to use the actual equation on the linked page. 
But even that is only an estimate. It assumes a calorically perfect gas. And it assumes everything is isentropic. Your real motor won't be. It also won't have constant pressure due to the burning of the solid propellant changing the chamber volume. 
So -- given an exit pressure and desired critical pressure (and associated temperature, density, and flow rate), you can figure out how much chamber pressure is needed, and then design a nozzle with the proper area ratios to ensure that the required exit pressure is met. 
