Kinetic energy of mass m1=12m1v12
Kinetic energy of mass m2=12m2v22
Total kinetic energy after collision
Kf=12m1v12+12m2v22
So, according to the law of conservation of momentum
m1u1+m2u2=m1v1+m2v2⇒m1(u1−v1)=m2(v2−u2) ............(1)
And according to the law of conservation of kinetic energy
12m1u12+12m2u22=12m1v12+12m2v22⇒m1(u12−v12)=m2(v22−v12) .............(2)
Now dividing the equation
(u1+v1)=(v2+u2)⇒u1−u2=v2−v1
Therefore, this is, relative velocity of approach is equal to relative velocity of separation.