logit-normal distribution query

#1
Given a logit-normal density function,

g(t)= exp( (-1/2) * ( (ln(t/(1-t)) - u) / s)^2 ) / (sqrt(2pi) * s * t * (1 - t))

where logit(t) ~ N(mean,stdev) ~ N(u,s), t is bounded (0,1), and the expected value of g(t) is E(t)=x and variance of V(t)=y, I need to determine u and s given x and y.

I don't think this is explicitly solvable. Any advice is appreciated. Thanks!

Sparkles