Engineering is a frame of mind. We study the technology in school, but that's not the only aspect to it. In fact, that's not even half of it. Other aspects include setting goals, budgets, design methods, life cycle maintenance, and forensics. Furthermore, if you're not always studying newer technologies, you'll soon find yourself out of a job.
The goal of an education is to lay down a theoretical base that you can use for studying new technologies and methods. Long after receiving my degree (many years), I'd get these flashes of insight that would relate my current situation to something we studied in class but didn't actually associate or apply to anything. While that theoretical base is helpful, it is not and can never be complete.
As such, the foundation that your degree lays for you helps --but it is not a defining issue. The math and the concepts are all very similar. Resonance is resonance whether it is mechanical, electrical, or atomic. Likewise, potential is potential, whether it is a column of water, a charge on a capacitor, or the pH of an acid.
I know more than a few engineers who got their start in other fields and who then began applying it to something completely different. Once you have learned some concepts, you can use what you know and your experiences to study others. For example, I didn't study anything about information theory in my college experience. However, I did open some books and study some fundamental concepts (Shannon's Limit, coding methods, the Walsh-Hadamard transform, etc...) so that I could understand what I was dealing with better.
Again, this is not about your education. That continues throughout your career. This is about the conceptual frame of reference for your career, not the actual work you do.