Question: What´s wrong with this piecewise solution?

I tried to solve the following nonlinear equation system:

with(Statistics):

Y9 := RandomVariable(LogNormal(a, b)):

solve({mu=Mean(Y9),(sigma)^(2)=Variance(Y9)},{a,b}, UseAssumptions) assuming a::real, mu::real, sigma>0, b>0;

The problem is that the conditions, which discriminate between the cases of the piecewise solution are puzzling, not to say impossible to meet.

E.g. at the end of the first row it says:

And(0 < sqrt(2*ln(sigma^2+mu^2)-4*ln(mu)), sqrt(2*ln(sigma^2+mu^2)+4*ln(-1/mu)) = 0)

which to my mind is impossible to meet since both ln(mu) and ln(-1/mu) should be real numbers!?

Does anyone know what is happening here, or knows a better way to solve this equation system while accounting for the assumptions above?

Thanks a lot.