Solve for x
x=-\frac{1-y}{e^{y}}
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1+xe^{y}=y
Swap sides so that all variable terms are on the left hand side.
xe^{y}=y-1
Subtract 1 from both sides.
e^{y}x=y-1
The equation is in standard form.
\frac{e^{y}x}{e^{y}}=\frac{y-1}{e^{y}}
Divide both sides by e^{y}.
x=\frac{y-1}{e^{y}}
Dividing by e^{y} undoes the multiplication by e^{y}.
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