What are chances I can find out how I got HIV if I haven't been tested in over 10 years?

Not good. You can look back and examine who your sexual partners were, whether you were using drugs at that time, whether you had a blood transfusion or transfer of other bodily fluids in an intimate manner, but confirming that this was the source will be nearly impossible. And, beyond that, what matters most is that you have recognized it and are going to be treated. Wish you well.