You need a dual mounting unit that will allow two seperate LNB's on the same dish (just that 10degree's is quite an odd split to use a dual LNB) This then can very easily be controlled via a simple diseqc switch.
One thing though that would worry me is the footprint of the sat at 38E. If the footprint is concentrating on SE europe then you might need a very large dish to get even a reasonable signal here in the UK. Will see if I can find the footprint for the sat in question
---------- Post added at 14:48 ---------- Previous post was at 14:43 ----------
Looking at the sat maps you should be fine with a 60cm dish
http://www.lyngsat-maps.com/hellas2.html
The sat in question is HellasSat2 at 39E, looking at the listing though half of the channels are encrypted
http://www.lyngsat.com/hellas2.html