A How do I solve y*exp(y)=[constant] for J using the Lambert W function?

[willDavidson]

TL;DR Summary

I would like to solve an equation that ends up in a form similar to y*exp(y)=[some constant]

I am trying to solve for J in the equation attached. I've also posted a link to the equation. The equation is to solve for J but both the left and right sides have J. I'm not quite sure how to solve that and it looks really messy so I simplified. Letting all of the terms equal either 0 of 1, I get J*exp(J)=2. The terms I simplified are below.
Let J01=1, q/kt=1, Rs=1, Rshunt=infinity, V=0

I'm stuck on what to do with this to solve for J so any help is appreciated.

https://www.pveducation.org/pvcdrom/characterisation/double-diode-model

 

[bigfooted]

The solution is the Lambert W function, which cannot be expressed in terms of elementary functions:

https://en.wikipedia.org/wiki/Lambert_W_function

There are also papers on using Lambert W for the solution of the double-diode problem, but I don't know anything about that topic, so I will not link any here.

By the way, I just checked on wolfram alpha, and it gives y=W(5) as the solution to y*exp(y)=5

 

[willDavidson]

The solution is the Lambert W function, which cannot be expressed in terms of elementary functions:

https://en.wikipedia.org/wiki/Lambert_W_function

There are also papers on using Lambert W for the solution of the double-diode problem, but I don't know anything about that topic, so I will not link any here.

By the way, I just checked on wolfram alpha, and it gives y=W(5) as the solution to y*exp(y)=5

Ahh thanks. I really wanted to know how to actually solve this thing so this will help a lot.