From the below equation, which is a sum of two exponential functions I would like to compute the common factor $n$
$$ d = \exp\left(\frac{-x}{n}\right)+\exp\left(\frac{-y}{n}\right)$$
Unfortunately, values $x, y$ are both significantly bigger than $n$, so I cannot use the approximation $e^x \approx 1 - x$, because it works only for small values of $x$. Is there any other way to compute value $n$, for fixed $d, x, y$ even approximately?