That's not an Identity!

Number Theory Level 2

If $$x$$ and $$y$$ are positive integers, and satisfy

$(x+y)!=x!+y!$

Find $$x$$ and $$y$$. Enter $$x+y$$ as your answer.

Notation: $$!$$ is the factorial notation. For example, $$8! = 1\times2\times3\times\cdots\times8$$.

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