I have got the equation
$$y = F(x)-x*G(x)$$
and want to solve it for $x$. So i am searching for something like:
$$x = F^{-1}(y)-yG^{-1}(y)$$
(which is wrong obviously)
In my context $F(x)$ is the probability density function and $G(x)$ is the survival function of a normal distribution. Therefore $F^{-1}(x)$ should be the cumulative distribution function and $G^{-1}(x)$ should be the inverse survival function.