To buy an .eu TLD (top level domain), EURid requires you to be either an individual (‘natural person’ ) living in the EU or an EU-registered company.
EURid has a list of registars, from whom you can purchase a .eu domain. They are available from some, but not all, major players.
When you register, check which email address the registrar wants to pass on to EURid, for WHOIS. EURid doesn’t allow privacy to extend to email addresses, but you can specify which one you wish to use for EURid. Alternatively, you can set up another email address and have the registrar change it – EURid doesn’t do this.
EURid produced a guidelines PDF on WHOIS, selling your domain etc.
My .eu Guidelines PDF