The elastic potential energy stored in a stretched spring is given by $U = \frac{1}{2}kx^2$ . The tension $T$ in the spring is equal in magnitude to the restoring force, so $T = kx$ . From this, the extension $x$ can be written as $x = \frac{T}{k}$. Substituting this value of $x$ into the potential energy formula, we get: $U = \frac{1}{2}k \left( \frac{T}{k} \right)^2 = \frac{1}{2}k \left( \frac{T^2}{k^2} \right) = \frac{T^2}{2k}$ Thus, the energy stored by the spring is $\frac{T^2}{2k}$.