are your two values, vc and vg, always as in the simulation?
that is, does vc always start less than vg and increase in an exponential(?) manner?
this implies there is only one solution
apparently you have an equation next to each of the blocks in your schematic
given whatever inputs you have, do you know the net equation for vc?
it may not be easy, but you should be able to solve constant = function of time
one way to get a symbolic solution is to use wolfram alpha
type in your equation, vc = f(t)
tell wolfram alpha to solve for t