The problem with the question is that, so far as I know, there is no official, universally agreed upon definition of what constitutes 'Eastern Africa.' Unless there are specific boundaries of a region known as 'Eastern Africa', there can't be a definitive list of nations contained within this region.
For instance, most maps of a region known as 'Eastern Africa' include the following nations: Burundi, Djibouti, Eritrea, Ethiopia, Rwanda, Somaliland / Somalia, Tanzania, and Uganda.
But other maps of 'Eastern Africa' include Sudan. And yet other maps don't include Sudan, but they do include Madagascar and Mozambique.
I'm sorry if this answer isn't very satisfying, but there it is.