A Problem from my book -9!

A conductor whose resistance is constant $R= 5 \ \Omega$ due to some reason is connected to a $5 \ V$ battery. The heat lost $Q$ to the surrounding due to radiations is dependent on both temperature of conductor $T$ at any instant and time elapsed $t$ as $Q= a(T - T_0) +bt^2$ , where $T_0$ is temperature of conductor at time $t=0$ , $a= 10 \ J/K$ and $b= 4 \ J/s^2$ . The conductor has a constant heat capacity.

Find the time after which the temperature of conductor becomes $T_0$ again. If $t= \dfrac XY$ , where $X$ and $Y$ are coprime integers, find $X+Y$ .