Solving Log Equation Double Integration - e^(e+1)

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Homework Statement

Do anyone know how to solve:
y=LN x
y=e+1-x

Homework Equations

y=LN x
y=e+1-x

The Attempt at a Solution

LN x=e+1-x
x=e^e * e^1 / e^x
x*e^x=e^(e+1)

then I don't know how to solve, must I solve it graphically?

Actually, the original question is :
Double integration
InIn x dxdy for the area bounded by y=e+1-x and y=LNx and x-axis

 

[QED Andrew]

Trial and error shows $x = e$ is a solution to $\ln{x} = e + 1 - x$. Closer inspection reveals the solution is unique because $\ln{x}$ is strictly increasing while $e + 1 - x$ is strictly decreasing.

I know not of an elementary technique for solving such an equation.

 

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Thanks a lot.