Question 1002272
<pre>
{{{e^x-x=2}}}

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 {{{y = e^x-x}}} and the
graph of the right side {{{y = 2}}}, and find where they
intersect

{{{drawing(400,400,-3,3,-3,3,graph(400,400,-3,3,-3,3,e^x-x),
graph(400,400,-3,3,-3,3,2),
circle(1.14619322,2,0.15),circle(1.14619322,2,0.13),circle(1.14619322,2,0.11),circle(1.14619322,2,0.09),circle(1.14619322,2,0.07),circle(1.14619322,2,0.05),circle(1.14619322,2,0.03),circle(1.14619322,2,0.01),

circle(-1.84140566,2,0.15),circle(-1.84140566,2,0.13),circle(-1.84140566,2,0.11),circle(-1.84140566,2,0.09),circle(-1.84140566,2,0.07),circle(-1.84140566,2,0.05),circle(-1.84140566,2,0.03),circle(-1.84140566,2,0.01) )}}}

They intersect at

(-1.8414056604369606378...,2) and 

(1.1461932206205825852...,2)

So the two solutions are approximately

-1.8414056604369606378... and 1.1461932206205825852...

Edwin</pre>