If you haven't studied the Lambert w-function,
then the only way to solve this is with technology,
such as with a graphing calculator.
Draw the graph of the left side
and the
graph of the right side
, and find where they
intersect
They intersect at
(-1.8414056604369606378...,2) and
(1.1461932206205825852...,2)
So the two solutions are approximately
-1.8414056604369606378... and 1.1461932206205825852...
Edwin