Engineering majors typically require 30-32 or so credits of math and natural science plus at least (often substantially more than) 45-48 or so credits of engineering science and engineering design. This means a minimum of 75-80 credits for the major, but many engineering majors at many schools require substantially more than that (up to about 100 credits out of the four year total of 120-128 credits). Some of the remaining space must be used for humanities and social studies general education courses.
The math and natural science will have some overlap with pre-med requirements, but (a) engineering majors typically have to take more advanced math than pre-meds, (b) engineering majors typically have to take a more math-intensive version of physics, and (c) engineering majors typically do not have biology (except biomedical), biochemistry, or organic chemistry (except biomedical or chemical) in their required science courses, and some may not have statistics (or at least as a well defined course that can be listed as such for pre-med purposes).