A solid sphere rolls at speed $v$ on a horizontal surface and elastically collides with an identical stationary sphere (line of centres horizontal). After friction restores rolling on both, their speeds are:

Elastic identical collision transfers translation only: just after collision, sphere 1 has $v=0$ but still spins ($\omega = v/R$); sphere 2 has $v$ but no spin. Friction restores rolling: for sphere 2, friction decelerates $v$ and spins it up — final $v_2' = (I/(I+mR^2))\cdot 0 + (mR^2/(I+mR^2))\cdot v = (5/7)v$. For sphere 1, friction accelerates $v$ from $0$, final $v_1' = (2/7)v$ (mirror calculation). Momentum sum $(2/7)v + (5/7)v = v$ ✓.