Conditional Formatting For Date

I have 2 columns that I need to set conditional formatting for. In one column (D) I have a date of when a person needs to be paid. In the next column (E) I have when the date of payment was or nothing indicating I have still not paid this person. What I need column D to do is have conditional formatting (im assuming this is the right way to do this) color the cell if we are late or if the person has not been paid yet according to the date in the E cells. Here is what I have so far:

(in cell D1)
Condition 1:
Cell Value is greater then =$E1
Color grey

Condition 2:
Cell value is less than =$E1
Color pink

He is where im running into the trouble. Condition 1 indicates that if cell D is greater then cell E then I have paid the person on time or sooner (grey). Condition 2 shows that if cell D is a date before the date in cell E then it turns pink indicating I was late on payment.

What I also need the condition to do is change cell D pink if there is no info in cell E, which is indicating that I still need to pay someone. So I tried a 3rd condition, but it doesn’t coincide with condition 1. I tried:

Condition 3:
Cell value is greater then 0
Color pink

What I need the 3rd condition to do is say if cell E has nothing in it then I need cell D to change to pink. Im assuming I need 3 conditions for this to work, but im not to sure.