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, $e \approx 2.71828$ .