Intuition pump: if the masses are equal and one isn't moving, then as per a Newtonian cradle, the moving ball stops completely and the other takes up its motion.

Also, hooray for Maxima!

(%i1) solve([m*v+mm*vv=m*w+mm*ww, m*v*v+mm*vv*vv=m*w*w+mm*ww*ww], [w,ww]);
(%o1) [[w=v,ww=vv],[w=(2*mm*vv+(m-mm)*v)/(mm+m),ww=((mm-m)*vv+2*m*v)/(mm+m)]]