We know from conservation of momentum or energy that energy (lets think about one quantity at a time) is conserved before and after collision. But how the energy is distributed between the bodies? I mean $1+3=4$ otherwise we can say $2+2=4$. Which distribution would be preferable?
It is easier to start with conservation of momentum, because even though total energy is conserved kinetic energy may not be conserved. For example if you collide two tennis balls covered in glue, they will stick to each other and the final kinetic energy will be zero (total energy is still conserved because the original kinetic energy ends up as heat in the two balls). Even in sticky collisions momentum is always conserved.
To calculate what happens in the collision you use the conservation of momentum to write down an expression linking the original and final velocities. If you know the coefficient of restitution you can write down a second equation linking the original and final velocities, and you just solve the two simultaneous equations to calculate the final velocities. This then tells you how the energy is divided between the two objects after the collision.