Whopping noise from open rear windows on 2010 Corolla LE

Yup, what they said.

I have found that, even with the front windows closed, opening the fresh air from the Heat-AC-Vent system reduces the rear-window buffeting. That has worked on two or three different cars, including a 2004 Camry. Gives nice fresh air in the front, with the windows closed so your hat doesn’t get blown off.