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Number theory Difficulty 3.0 AMC 10/12 Prove it Canada

A number is divisible by 9 if the sum of its digits is divisible by 9. For example, the number $19\,836$ is divisible by 9 but $19\,825$ is not. If $D\,767\,E89$ is divisible by 9, where $D$ and $E$ each represent a single digit, what are the possible values of the sum $D + E$ ? Explain how you obtained your answer.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.