According to the equation for the coefficient of restitution

$e=\frac{\mathrm{velocity} \mathrm{of} \mathrm{separation} \left(\mathrm{after} \mathrm{collision}\right)}{\mathrm{velocity} \mathrm{of} \mathrm{approach} \left(\mathrm{before} \mathrm{collision}\right)}$

 $e=\frac{v_2-v_1}{u_1-u_2}$ along the line of impact.

From the figure, $e=\frac{v_2-0}{u_1\cos \theta -0}=1$

$u_1\cos \theta =v_2$

According to the conservation of momentum along the line of impact 

$m_1{u}_1\cos \theta =m_2{v}_2$

as $u_1\cos \theta =v_2$

$m_1=m_2$