A system of exponential and logarithmic equations

Here is an interesting system of equations problem.

Find x and y:
$$
\begin{align}
log_{3}(x+y)+log_{3}(x-y)&=1 \nonumber\\
4^{\frac{x}{y}+\frac{y}{x}}&=32 \nonumber
\end{align}
$$

The solution is super interesting and is a great example of how simpler paths to solution are often just hiding out or are buried in something that looks quite a bit more complicated. Have a look at the solution HERE!