How to connect Macbook Pro 2015 and 2 x Dell U2518D monitors
No, you do not need Mac drivers for this monitor to function.

I think the problem is your cable. I would suggest using the cable that came with the monitor to connect the laptop and the display. That cable is a Mini DisplayPort to DisplayPort cable. If this is actually the cable you've used (and not HDMI as you mention), then try getting an alternative cable to test with.

All you need to do is to plug that cable into the laptop and the monitor, and you should get a picture. You might need to set the input on the monitor to Mini DisplayPort if you have disabled the auto function.

If that fails to work with a good cable, try rebooting the laptop with the cable plugged in. That should definitely not be necessary, but just to test out every option.