Invert the softmax function

Is it possible to revert the softmax function in order to obtain the original values $x_i$? $$S_i=\frac{e^{x_i}}{\sum e^{x_i}} $$ In case of 3 input variables this problem boils down to finding $a$, $b$, $c$ given $x$, $y$ and $z$: \begin{cases} \frac{a}{a+b+c} &= x \\ \frac{b}{a+b+c} &= y \\ \frac{c}{a+b+c} &= z \end{cases} Is this problem solvable?