Hm I thought .EU domains cost more then ten bucks, just checked at namecheap it costs $11 at this dynadot something below $10. Do you know if EU domains does have whois privacy protection option? Also if I'm right you need to be in (or have a company in) EU to register an EU domain.
I would say, according to that page YOU CAN... as long as you have presence in Europe, let's say your business office located in any European country, but as an individual living elsewhere, no, you can't indeed.
Hm adexpert10 said that he is not from Europe, and I think he would mention it if he had a company in EU.