Can AND and OR be used in the formula of a conditional formatting?

Cell E3 contains a date. I have set the E3 conditional formatting as follows:

CF1 formula is =+E3="" format cell with black font, white cell color
CF2 formula is =E3<=TODAY() format cell with yellow font, red cell color
CF3 formula is =E3TODAY() format cell with black font, green cell color

I would like CF1 formula to be =+E3="" OR D3<"" format cell with black
font, white cell color, but I get a syntax error message.

Is there other syntax I should use, or is this not possible?

TIA
David R.