No 0's at all!

$$\color{red}{A}$$ and $$\color{blue}{B}$$ are whole numbers that do not contain 0 as a digit when expressed in base 10

If $$\color{red}{A} \times \color{blue}{B} = 10000,$$ then what is $$\color{red}{A}+\color{blue}{B}?$$

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