MHB Lambert W Function: Solving $r=ue^u$

[Dustinsfl]

Based on Pickslides reference to the Lambert W function, I am now trying to solve this:

$$
r = \frac{q\left(1-\exp\left\{-\frac{u^2}{\varepsilon}\right\}\right)}{u(q-u)}
$$

So now I have this in the form $r = ue^u$ and I need to transform it to $u = w(r)$

I am not quite sure on how to do that though.

 

[Sudharaka]

So now I have this in the form $r = ue^u$...

Hi dwsmith, :)

Did you transform the original equation into the form \(X=Ye^{Y}\) ? If so can we please see the result?

Kind Regards,
Sudharaka.