What do "e" "-" "C" and "E" mean in this output?
CCCEEE etc. are the secondary structural elements. In this case, the C refers to non-strand and non-helix regions i.e loop regions rather than a coiled region. The C or E usually refers to whether the residue is coiled (C) or part of a strand (E). H would be used to denote a helix, however, in the question, it appears that there are no helices. These letters are often different in different software: it's merely a point of semantics between different software. 

e or - refers to if the amino acid at that position is exposed or not (- = buried).

For the method, here is the COBEpro paper, although it does seem very technical. The help page has more easily accessible information on the output.