Repeating Power

Calculus Level 4

\[\Large{ e^{x+e^{x+e^{x+e^{x+\cdot^{\cdot^\cdot}}}}}=10}\]

Find the value of \(x\) satisfying the infinitely nested function above.

Give your answer to 3 decimal places.

Enter 0.666 if you come to the conclusion that no such \(x\) exists.

Clarification: \(e\) denotes Euler's number, \(e \approx 2.71828\).