Were two handed swords used in Eastern Europe in Medieval times? Particularly in Byzantine, the Romania region, and Byzantine influenced nations.
The short answer: yes. They were less common than one-handed swords, but they were there.
Two possibly Byzantine examples:
These warrior saints are dressed in Byzantine military fashion, and both carry two-handed swords.
There are many examples in Marko Aleksić, Mediaeval Swords from Southeastern Europe. Material from 12th to 15th Century (2007): https://www.academia.edu/496513/Mediaeval_Swords_from_Southeastern_Europe._Material_from_12th_to_15th_Century_2007_by_Marko_Aleksi%C4%87 (again, outnumbered by the single-handed swords). One example: Sword from Serbia, 23cm long hilt, 95cm blade
One notable style of two-handed sword is the two-handed Hungarian sabre. Example: 15th century Hungarian sabre, 22cm hilt, 87cm blade (3rd from left), pg 171 in Heinrich Müller & Hartmut Kölling, Europäische Hieb- und Stichwaffen, Militärverlag, Berlin, 1982.
Another example, from Slovenia, with a detailed study of the sword downloadable as a pdf: https://www.albion-swords.com/swords/johnsson/sword-museum-ljubljana.htm