Equations-EMT

Algebra Level 2

$\large \begin{cases} e^{mt} = emt+mt^e-1 \\ e^{mt} = emt+tm^e-1 \\ \ln(emt)=1 \end{cases}$

Clarification: $$e \approx 2.71828$$ denotes the Euler's number.

Let $$m$$ and $$t$$ be positive real numbers satisfying the system of equations above, find $$m+t$$.

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