What wheel is this and how big of a tire can I run?

No, "E-T" never made wheels like that. In this case, being a modern design of wheel, the "ET19" refers to the wheel offset in millimeters. ET is the abbreviation for the German word Einpresstiefe. I would guess these 4" wide wheels with a 19mm offset have a backspacing of about 82.5mm or 3.25".