O. Sluciak:
"On the roots of a^x+a^-x =x";
2013; 5 pages.
We provide an analytical closed-form solution of the exponential equation ax + a−x = x for a specific value a, discuss the number of roots in general case, and provide bounds on the roots.
http://publik.tuwien.ac.at/files/PubDat_223437.pdf