So, I got my wedding band....

It's beautiful. And I don't think the gap is a big deal at all. If it really bothers you, you can either buy a low spacer band to fit between your e-ring and w-band that will close the space a bit. Otherwise, consider wearing your e-ring on your right hand.

My e-ring is super detailed with pave diamonds and hand engraving. I think wearing a band on the same finger will only take away from the e-ring's beauty, so I will be wearing my rings on separate hands.