Hello, camherokid!

Solve for x: .e^x - e^{-x} .= .2

Multiply by e^x: .e^{2x} - 1 .= .2·e^x

And we have: . (e^x)² - 2·e^x - 1 .= .0 . . . a quadratic equation

. . . . . . . . . . . . . . . . . . . . . . . . __________

. . . . . . . . . . . . . . . . . . . . 2 ± √2² - 4(1)(-1)

Quaratic Formula: . e^x .= . ----------------------- . = . 1 ± √2

. . . . . . . . . . . . . . . . . . . . . . . . 2(1)

Since e^x is positive: . e^x .= .1 + √2

. . Therefore: . x .= .ln(1 + √2)