Question 831686
you have e^-x = 1/e^x (convert)
So the equation will become
e^x - 1/e^x = 1 
multiply e^x like you said
{{{e^x*e^x - 1 = e^x}}}
{{{(e^x)^2 - e^x - 1 = 0}}}
Then you can let e^x = a and the equation will become
{{{a^2 - a - 1 = 0}}}
You can solve this equation using quadratic formula, then you will get two answer
{{{a}}} = {{{(1+sqrt(5))/2}}}
and {{{a}}} = {{{(1-sqrt(5))/2}}}
Remember you let e^x = a? Now change a into e^x 
You have {{{e^x}}} = {{{(1+sqrt(5))/2}}}
Then you use natural log on both side, you will have
{{{x}}} = {{{ln((1+sqrt(5))/2)}}} and then use calculator to find it
And then you find another answer with {{{e^x}}} = {{{(1-sqrt(5))/2}}} using the same method
TA-DAH