There is no "engineering math" separate from "math". To learn good math as an engineer, you have no other way but to understand math from its nature.
The first course you learn is probably real analysis. In my opinion, no one masters real analysis when the topic is met the first time. Don't worry if you feel you have done the homework and passed the exam but don't have a clear clue of what it is for. Real analysis is the topic that opens the door to modern math, as compared to what you learned at high school. The core technique you need to master is formal reasoning, or proof construction. Learning first-order logic systematically would definitely provide you with a clearer understanding of this technique. Once you have mastered the tool for formal reasoning, you are able to appreciate proofs written in English in a more fundamental way. Without the knowledge of first order logic, long proofs cannot be truly understood, especially when there are many levels of existential and universal propositions. After understanding first-order logic and probably a little set theory, it is the moment you review real analysis and tell why learning the material the first time is not really helpful.
You will definitely learn linear algebra. This is the course you learn linear spaces and transformations between linear spaces. It is the first time you understand that modern math is concerned with the structures of specific types of sets with operations defined on them. Some universities teach this topic with an emphasis on matrices and vectors. I don't quite agree with this type of education for linear algebra. I would recommend learning this topic from the bottom up. That is, understanding clearly the concepts of linear transformations, and then, associate them with matrices and vectors. With the proof capability you learned in real analysis, you should be able to understand and construct proofs more easily in this course.
Then you will need to know how to model the world of uncertainty. Probability theory and statistics are what you need to learn. Again, pay more attention to theory and do not focus on data at the beginning. You need to rigorously construct your understanding of events, probability, random variables, expectation, convergence, etc. Do note that the concept of convergence from real analysis plays a significant role in the analysis of estimators.
With all these basic course learned and understood, you should learn optimization. Optimization tells you how to make the best choice with a definition of cost in mind. It is widely used in signal processing, control, machine learning, computer graphics, etc. In fact, many rigorous engineering papers published on good conferences or journals are optimization in nature.
With these topics learned and practiced in everyday applications, you should be able to deal with most engineering problems in electrical engineering or computer science in a very rigorous way. With these describing languages in mind, you should solve real problems with coding. Now, coding is a technique that connects knowledge and capability. With a good understanding of math, you should be able to write high-quality codes.