Can we get an analytical solution to this equation involving the Lambert W function?

Question

Can we get an analytical solution to the variable $t$: $$H\left(1+W\left(A\exp\left(Bt\right)\right)\right)=1+W\left(X\exp\left(Yt+Z\right)\right)$$ $W(x)$ is the Lambert W function.$A$ $B$ $X$ $Y$ $Z$ $H$ are all constant and positive.

What about the approximate solution? The $t$ is a positive real number.

Answer 1

Let $y=1+W(A\exp(Bt)$, then $A\exp(Bt)=(y-1)\exp(y-1)$
You can find $t$ as a function of $y$, and put that into the right-hand side.
$H(y)=1+W(...)$