Hello, I'm Nico from Germany.
I was able to find one solution to this equation using the W function but when I graphed both terms I noticed there's another solution. I tried really hard but I wasn't able to find it by calculation. (Yes, WolframAlpha showed both solutions). Seems like an interesting problem.
To find the solution using the W Lambert function, you had first to factorize and simplify by (x+2). So (x+2)=0 => x=-2 is your "mysterious solution".
The other solution is x=W(sqrt(3))+2, as you probably found.
God forbid my stupidity
Es passiert jedem. 😉