$x!=y, \space x ∈ ℝ$
Is there a formula to find the exact value of $x$ in this case, assuming that we know the value of $y$?
I could do $L(x)/W(\frac{L(x)}{e}) + \frac{1}{2}$ where $W$ is the Lambert $W$ function and $ L = \ln(\frac{x+c}{\sqrt{2\pi}})$, but that only gives an approximate value, and not an exact one.
In general, the inverse of the $\Gamma$ function is not known to possess a closed form expression, if that is what you're asking. The best you might hope for is an infinite series/product expansion, and/or a continued fraction representation.