Explanatory essay has no bias or opinions involved. It is made up of evidence and justifications.
Argumentative essay is when you are trying to persuade the reader or audience about how your opinion is right. you must also provide a counterclaim to show you have thought about all possibilities of what you are talking about.
an explanatory essay tries to explain a concept, or problem without trying to discredit or mention another writing piece, or article. an argumentative essay takes an article or piece of writing and has detailed facts, or reasons as to why that article is wrong.