Do you know Soumava's Algorithm?

Calculus Level 5

\[ \large x^y = y^x = 43 \]

If \(x\) and \(y\) are distinct positive real numbers satisfying the equation above, find \(\lfloor 100(x+y) \rfloor \).

You are allowed to use computer assistance.

You might refer to Soumava's algorithm.

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