Solution of $\exp(z)=z$ in $\Bbb{C}$. I have posted a related question here. I thinkg this one is more interesting: 

What about the solution of $\exp(z)=z$ in $\Bbb{C}$?

My try :
$z \mapsto e^z - z$ is entire non-constant.
Perhaps $z \mapsto e^z - z$ can be developed in Weierstrass product.
Also any numerically approach will be very interesting.
Thanks you in advance.

If
$$z = e^z$$
then
$$-ze^{-z} = -1$$
so
$$-z = W(-1)$$
and thus
$$z = - W(-1),$$
where $W$ is any branch of the Lambert W function.
