A metal wire length L, cross-sectional area A and Young's modulus Y is stretched by a variable force F. F is varying in such a way that F is always slightly greater than the elastic forces of resistance in the wire. When the elongation in the wire is l, up to this instant 

In this question, the applied force is not constant. Let us consider at any instant the wire elongates by x. Then work done by F to elongate it more by dx is

$\mathrm{dW}=\mathrm{Fdx}=\frac{\mathrm{YAx}}{\mathrm{L}}\mathrm{dx}[\mathrm{x}\ll \mathrm{L}]$

$\mathrm{W}={\int }_0^{\mathrm{l}} \frac{\mathrm{YAxdx}}{\mathrm{L}}=\frac{{\mathrm{YAl}}^2}{2\mathrm{L}}$

As internal restoring force and applied force are almost same (equal and opposite), numerical value of work done by these two forces would be equal.