While some interview problems rely on knowing a trick (and I would argue that these are poorly chosen problems that reveal little about candidates except whether they know the trick), most problems can be solved with a good understanding of computer science and engineering fundamentals. It requires practice, however, to learn how to break a problem into its components, come up with solutions for the components, and then weave them into an overall solution.
Like you, I'd been in the industry for more than a decade. Solving interview problems is very different from professional work. So, you'll probably need to practice your interview-problem-solving skills. I know I did.
What I did was put a whiteboard on my wall and solved problems on it. I solved the problems blind, drawing them randomly from a book (Elements of Programming Interviews was my primary source). I video recorded myself and reviewed the recordings to help me refine my spoken thought stream and to learn to avoid stumbles and long stretches of silence. I then practiced in this way for a month, on and off, until I became good at it.
Best of luck!