m1 = 0.198kg, m2 = 0.304kg, v1i=1.40 m/s, v2i=-0.404 m/s
v1f=? v2f=?
So according to conservation of momentum final momentum equals initial momentum so:
m1*v1i+m2*v2i = m1*v1f+m2*v2f
when you plug in variables you'll be left with 2 unknowns, therefore you need one more equation to solve.
Since the collision is ellastic, use this formula:
(v1i-v2i) = v2f-v1f
solve for one variable and plug back into the other equation and solve.
then plug back into the equation to get the second variable.