A colloquium talk should consist of three parts of roughly equal length:
(1) An introduction understandable by any beginning graduate student in the department, both those in EE and in CS. This is where you state the motivation of the problem, and outline what you achieved. Not all epsilons and deltas needed here. No area-specific prior knowledge should be assumed.
(2) A middle part that is accessible to every grad student and faculty member in your discipline (EE or CS). Undergraduate background in that discipline can be assumed.
(3) A last part addressed to faculty members and advanced grad students in your subarea, providing additional details, highlighting important issues, explicating the significance of the material.
(If you are in group 1 and are watching a talk, parts 2 and 3 are useful in getting some feeling for how deep the area is, and to see how others react to it. In any case, you didn't waste your time, since (1) was accessible.)
It is hard to get people to agree to structure a talk as above, but one may always suggest it when inviting speakers.