I resolved my issue by unplugging my USB cable from my UPS battery and restarting. Once I did this, airplane mode disappeared from my system.
I'm guessing something monitoring power levels caused Windows 10 (in my case, the UPS battery monitoring) to activate airplane mode. So if you don't have a UPS battery, do you have anything else that may report/monitor power levels on your system - maybe that's the cause of airplane mode being activated?
Notes: Dell Vostro with wifi and bluetooth. I have had my PC for over a year and upgraded to Windows 10 several months ago. I'm guessing some sort of update may have triggered this problem.
Hope this helps.