Mathematics is not science either, granted it is used by scientists but the two are separate disciplines. Yes scientists can also be mathematicians and vice versa, there is no brick wall separating the two disciplines
Science is the process of making hypothesis to understand the universe, and if they can be proven false they are dropped or changed into another hypothesis that works better. That is the process of science. Engineering uses those principles from the Scientists and apply them to real world problems.
I recommend another book https://www.amazon.com/Spectrum-Belief-Fraunhofer-Transformations-Technology/dp/0262527235
The author was my professor at college. This book lays out the confusing lines of difference between engineering and science. You are hardly the first who have confused this issue.