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how do I differentiate an implicit equation

I'm trying to differentiate an implicit expression

$x e^{y} = x -y$

This is my sagemath code

x = var('x')
f(x,y)= x*e**y - x + y

Sagemath Answer is $\left( x, y \right) \ {\mapsto} \ \left(e^{y} - 1,\,x e^{y} + 1\right)$

But the actual answer is $\frac{1 - e^{y}}{x e^{y} + 1}$

How do I get the actual answer using sagemath?