Try purdue university + indiana kelley. They have such programs spanning over 5 years. You can choose the master type among few of them from purdue and continue with kelley mba.

The choice are so limited, a dual degree will probably not be the fastest, cheapest or best way to do that.

Yes, the Purdue/Kelley dual program is probably one of the best.

Also consider ASU Carey, which allows allows online MBA students to pair that degree with an MSE Electrical Engineering or an MS in Industrial Engineering.

However, I would question the usefulness of doing both of these degrees; all but a small subsection of MBA candidates would probably find an additional master's degree in engineering to be overkill. Usually, students from the engineering disciplines who pursue MBAs already have enough of the technical knowledge, and really just need the strategic and soft skills that only an MBA can deliver.