Replacement has only 2 wires coming from it and they are both coated in white. So how do I tell which one to hook up to which one?

What colots are they? & compared to the wiring you have, how many wired ate there..?

You probably have a zip cord wire, common for chandeliers and other similar lights. Look at the wire: One side should be smooth and one side has ridges. The ridged side goes to the neutral(white) and the smooth side to the black.

He ma0641, hope all is well, if the wiring "appears" identical, then the wire attached to the outer shell is the neutral.(continuity tester or meter)
Above post made by ma0641 is good on about 99.9% of what you will run into. Rarely they are identical, then they need to be rung out.