Last month I took my final exam for accounting online. My grades in the class are very good as I have a tutor for the class. I got an email from my professor telling me that she had to talk to me and I assumed it was because I did very well on the final, but when we talked she told me that I was getting taken to the board for academic misconduct because the written part of my exam (solving equations) was "almost identical" to another students. She said after reviewing she noticed that our midterm exams were also almost identical. I did not cheat, I don't know what I got on the exam as she would not tell me, or who the other student is. I would not be worried as I know that I am not guilty, but I have already talked to the board about plagiarism as there was a mix up with some homework in a previous class (it was not stated it was individual work and I worked on it with a classmate) it was an honest mistake and they just gave me a warning. Anyways, that really stresses me out as the teacher claims "there is no way this could be a mistake" but she won't let me know who the person is or what the similarities in our tests were? I feel like I have no way to prove my innocence.
It isn't up to you to prove your innocence. It is up to your instructor to prove your guilt. Insist that you did nothing wrong, assuming that is the case. Don't try to explain how you aren't guilty, but do explain, if asked how you solved any questions on the exam.
Let me note two things. Two correct answers are frequently likely to be the same, as that is just the nature of truth.
Second, all of the students had the same instructor and learning materials, so it is natural that they work in similar ways. It is natural that they approach problems in the same way. It is almost inevitable that there will be overlaps in how they solve problems.
No one can guarantee that injustice won't be done here, but similarity is not proof. Even using the same phrasing, if it is similar to that of the professor or the learning materials, is completely natural and to be expected. Especially from the better students.
You have a difficult task and can only suggest that if there is another faculty member who would be willing to speak for you at any hearing as your advocate, then it might make a difference. It is hard to stand alone against authority.
Also note that in technical subjects, there is frequently the situation that there are a limited number of ways to express something correctly. It is why some things in mathematics, for example, can't be copyrighted.
My personal opinion that a statement like "there is no way this could be a mistake", is both foolish and biased.