Solve for x
x=\frac{z}{e^{y}}
Solve for y
\left\{\begin{matrix}y=\ln(\frac{z}{x})\text{, }&\left(z<0\text{ and }x<0\right)\text{ or }\left(z>0\text{ and }x>0\right)\\y\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.
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xe^{y}=z
Swap sides so that all variable terms are on the left hand side.
e^{y}x=z
The equation is in standard form.
\frac{e^{y}x}{e^{y}}=\frac{z}{e^{y}}
Divide both sides by e^{y}.
x=\frac{z}{e^{y}}
Dividing by e^{y} undoes the multiplication by e^{y}.
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