You should check out Case Western Reserve University…in particular the think[box].
It combines both of what you are interested…the chance to invent something but also be an entrepreneur.
Larry Sears and Sally Zlotnick Sears think[box]
Case Western Reserve University’s center for innovation and entrepreneurship provides a space for anyone - students, faculty, and alumni and members of the community - to tinker and creatively invent.
e.g. https://www.cleveland.com/akron/index.ssf/2018/04/case_western_reserve_universit.html
Case also has a Single Door Admission Policy so if you started in engineering and wanted to swtich to business, you can…you don’t have to apply to the business school. You can also take business classes as an engineer.
Also they have a program where you cn get an integrated BS(engineering) and MSM-Finance degree.
https://weatherhead.case.edu/degrees/undergraduate/academics/finance/integrated-program
Obtain your BA/BS degree and an MSM-Finance degree in as little as four years in this integrated study program. This program is strongly recommended for BA/BS students (CWRU undergraduates only) who desire to leverage their quantitative and analytical skills developed during their undergraduate studies with specialized skills obtained from a master’s in finance.