"To address the question", "To answer the question". What's the difference?
To address a question is to deal with a question, not necessarily to answer it.
To answer a question is to provide the information requested in the question.
See this link.
People who say address the question when they mean answer the question are being pretentious.
You can address a question without answering it. If, for example, allegations are made against a person and a central question comes up, then the person can address the question without actually answering it.
Also, if we can't answer a questions, it doesn't necessarily mean that we can't say something that might be useful about the topic in question. So we address the question.