Is there a closed form solution to $e^{-x/b}(a+x) = e^{x/b}(a-x)$? I have the following equation
$$e^{-x/b}(a+x) = e^{x/b}(a-x)$$
where $b > 0$, and $a > 0$
I need to solve for $x$. I can do it numerically, but would prefer if there was a closed form solution.
It seems to me that there likely is no closed form solution, but thought I'd ask the experts here, just in case.

Simple rearranging of the equation shows that the main theorem of [Lin 1983] can be applied that implies that the equation doesn't have solutions that are elementary numbers.
Simple rearranging of the equation gives
$$\frac{2a-bz}{2a+bz}e^z=1$$
This shows that the equation is in a form that is not solvable in terms of Lambert W. But the equation can be solved by Generalized Lambert W:
$$z=W(^{+\frac{2a}{b}}_{-\frac{2a}{b}};-1)$$
$-$ see the references below.
$\ $
[Lin 1983] Ferng-Ching Lin: Schanuel's Conjecture Implies Ritt's Conjectures. Chin. J. Math. 11 (1983) (1) 41-50
[Mezö 2017] Mezö, I.: On the structure of the solution set of a generalized Euler-Lambert equation. J. Math. Anal. Appl. 455 (2017) (1) 538-553
[Mezö/Baricz 2017] Mezö, I.; Baricz, A.: On the generalization of the Lambert W function. Transact. Amer. Math. Soc. 369 (2017) (11) 7917–7934 (On the generalization of the Lambert W function with applications in theoretical physics. 2015)
[Castle 2018] Castle, P.: Taylor series for generalized Lambert W functions. 2018
