Induced emf / back emf in an inductor coil is given by 

$\left|\mathrm{\epsilon }\right|=\frac{\mathrm{Ldi}}{\mathrm{dt}}$

$\Rightarrow 25=\mathrm{L}\times \frac{\left(25-10\right)}{1}$

$\Rightarrow \mathrm{L}=\frac{25}{15}=\frac{5}{3}\mathrm{H}$

Energy of inductor is given by

$\mathrm{E}=\frac{1}{2}{\mathrm{Li}}^2$

Energy change $△\mathrm{E}=\frac{1}{2}\mathrm{L}\left({{\mathrm{I}}_2}^2-{{\mathrm{I}}_1}^2\right)$

$\Rightarrow ∆\mathrm{E}=\frac{1}{2}\times \frac{5}{3}\left[625-100\right] \mathrm{J}$

$∆\mathrm{E}=437.5\mathrm{ }\mathrm{J}$