Answer
The ball whose initial velocity is $+7m/s$ has a final velocity of $-4m/s$ and the other one has a final velocity of $+7m/s$.
Work Step by Step
2 balls are identical, both of which has mass $m$. One ball has initial velocity $V_0=+7m/s$, and the other has initial velocity $v_0=-4m/s$
Using the principle of conservation of total linear momentum, we have $$m\vec{V_0}+m\vec{v_0}=m\vec{V_f}+m\vec{v_f}$$ $$\vec{V_0}+\vec{v_0}=\vec{V_f}+\vec{v_f}$$ $$\vec{V_f}+\vec{v_f}=+7-4=+3 (1)$$
Since the collision is elastic, the kinetic energies are conserved, too: $$\frac{1}{2}(mV_0^2+mv_0^2)=\frac{1}{2}(mV_f^2+mv_f^2)$$ $$V_0^2+v_0^2=V_f^2+v_f^2$$ $$V_f^2+v_f^2=49+16=65 (2)$$
Solving (1) and (2), we get $\vec{V}_f=-4m/s$ and $\vec{v_f}=+7m/s$
