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

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, \(e \approx 2.71828\).

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