Before I checked the answer, I calculated the recoil speed of the gun. And I set the equation using conservation of momentum to find the velocity of "you+gun".
i.e (M bullet * V bullet / M gun) * M gun = M you+gun V you+gun

But I don't know why the final answer is the Kinetic energy from the gun after the bullet is fired minus the Kinetic energy of "you+gun" after the impact.

By conservation of momentum, you have calculated the the momentum of the system directly after the after this inelastic impact. By looking at the kinetic energy before & after the collision you will notice that energy is lost somewhere; ask yourself where this energy has gone.

You also have to assume that no energy is lost during the time it take the rifle to you.