homework and exercises - Final velocities of a two point-masses in inelastic collision

Two particles of same mass in a 2D frame collide with known initial (i) velocities. I would like to know the final (f) velocities of them after the collision.

As in any other collision, momentum is conserved after the collision. Writing in components:

$$v_{x,1}^{i} + v_{x,2}^{i} = v_{x,1}^{f} + v_{x,2}^{f}$$ $$v_{y,1}^{i} + v_{y,2}^{i} = v_{y,1}^{f} + v_{y,2}^{f}$$

The total energy (not the mechanical) is also conserved. K accounts for the thermal energy.

$$v_{x,1}^{2,i} + v_{y,1}^{2,i} + v_{x,2}^{2,i} + v_{y,2}^{2,i}= v_{x,1}^{2,f} + v_{y,1}^{2,f} + v_{x,2}^{2,f} + v_{y,2}^{2,f} + 2 \cdot K/m$$ I obtain with this 3 equations for 4 unknown quantities, the x and y components of the velocities of particle 1 and particle 2. How could this be solved?. What information should I add? I can only think of modelling the collision with a potential of some kind.