So I'm reading my textbook and there's a problem asking what the muzzle speed of a projectile would be if the gun it is being fired from is free to recoil. I'm given the muzzle speed of the projectile when the gun is stationary, the mass of the projectile, and the mass of the gun. I'm also told that the kinetic energies of the system is the same for both cases. How is a problem like this solved? Every equation I've thought of so far ends up with two variables (the projectile's new speed and the gun's free-to-recoil speed).