Separation becoming too large will be considered as separation becoming infinity...

 

now apply conservation of energy...

 

initial KE = 0

initial PE = Kq₁q₂/r

 

final PE = 0            as r becomes infinity..

so we can find final KE.... now as the particles are identical in all respect... both will have same final velocity.... use final KE to get this velocity..

 

hope you can do the calculations... do tell me if u cant....