No 0's at all!

A\color{#D61F06}{A} and B\color{#3D99F6}{B} are whole numbers that do not contain 0 as a digit when expressed in base 10

If A×B=10000,\color{#D61F06}{A} \times \color{#3D99F6}{B} = 10000, then what is A+B?\color{#D61F06}{A}+\color{#3D99F6}{B}?

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