Index/Match - compare two ranges though

My objective is to find the date/time in A column when cell E is less than D or D is less than E, based upon the If criteria.

I tried using:
INDEX(WrkStName!$A$3:$A$100000, MATCH(1,(RANGE1 < RANGE 2)
(The actual formula is in the attached sample. For some reason, it would not let me post here, calling it HTML code (even when using [Code]))

But my formula did not work. How should I do it correctly?

I thank you for your guidance in advance. Example sheet attached (the ranges go for 100,000 rows, but reduced for simplicity).

Wow, thank you. I will give that a try.

Another related question. How would I do that with Match using multiple criteria for a different formula? Do I need to do another Match inside this Match?

Right now I have

HTML Code: 

Okay, Actually, I did have exact match setup. So then you confirm that doing it this way with exact match works?

Again, thanks for all your help!