There are some courses in English, e.g. in computer science, engineering physics etc.

Alternatively, there are so called studienkollegs (http://www.studienkollegs.de/home.html), where you can learn German. Actually, I have a friend from Hungary who did this. But she had a husband who earned money. After about a year you can be ready to start studying. Costs for the course (incl. living costs for a year) would be around the 10000EUR you mentioned. You can work to cover some of it, though there may be restrictions on when you are allowed to work. There may be ways for foreigners to finance their studies with a credit (look at https://www.kfw.de).

Additionally, there are institutions at the university that might be of help. Look for 'international students office' for any university you are interested in.