Congratulations on all your achievements! As a former double major in music and engineering, I can tell you that it's not impossible... but it's pretty close! There are indeed some fields where you can try to combine engineering and music, such as audio engineering or architectural sound design (designing concert halls, etc.), or you can even try my field of speech recognition where if not music you can at least try to integrate acoustic features with information technology.
I think in the end though, the real question here may be: can you still let music be a priority if you study engineering and NOT music? And the answer is, of course! In fact, often it can be easier! Most likely what you really plan for the future is not in reality to be at Google by day and the San Francisco Symphony at night. I found that I spread myself so thin trying to get adequate practice while keeping up with problem sets that I no longer found playing as relaxing and enjoyable as I once had. Once I made the decision to focus on engineering and reduce music to a minor, I felt I was able to be a better engineer and though I played less, found music to again be the enjoyable release it used to be. Without a formal program you do have to be more proactive to find time to practice and ensembles to play with, etc., but you may be surprised at all the options you find. And of course, when life gets really busy, I can't think of a better way to relax than to take a night off and enjoy a performance by the professionals!