jmc

We note that $\sqrt{9\cdot 9^t}=3\cdot 3^t$. The equation becomes: $$\begin{array}{rl}3\cdot 3^t+3\cdot 3^t& =18\\ \Rightarrow 6\cdot 3^t& =18\\ \Rightarrow 3^t& =3.\end{array}$$Therefore, $t=\boxed{1}$.