A 38E is a 38 band with an E cup — a full cup. The band does most of the work (around 80% of your support), so if it rides up at the back or the straps dig in, it's the band to fix, not you.
We cut 38E for fuller busts, part of our full 38D–38K range. Not sure 38E is your size? Book a personalized fitting and we'll get it sorted.