Nonlinear equations are tough. You can't guarantee they have a solution and there's no single trick or method for finding the solution. If Mathematica doesn't find a solution, then its pretty likely that a symbolic solution doesn't exist. I wasn't able to find a simple way to improve the equations. You can either:

• Simplify the equations somehow,usually by linearizing something like a Cosine or Sine.
• Try using a numerical method to search for a solution. NSolve or FindRoot can be used here.