Stored energy in capacitor is

$U=\frac{q^2}{2 C}$

and charge of capacitor in an $R C$ circuit during discharging is

$q=q_{0 } e^{-t / R C}$

Combining both, we have

$U=\frac{q_0^2}{2 C} \cdot e^{-2 t / R C}=U_0 e^{-2 t / R C}$

Given, $\quad U=\frac{U_0}{2}$

So, $\quad \frac{U_0}{2}=U_{0} e^{\frac{-2 t}{R C}} \Rightarrow e^{\frac{-2 t}{R C}}=\frac{1}{2}$

$\Rightarrow \frac{-2 t}{R C}=\ln \frac{1}{2}$

$\Rightarrow t=\frac{1}{2} \cdot R C \ln 2$