Don't quote references or variables, otherwise what you're passing to the function as criteria is literally "Eng_ID" and not the value that Eng_ID contains. Try
=DLookUp("Eng_Phone","TBL_Engineers","Eng_ID='" & Eng_Combo & "'") and that presumes that the criteria is text. If the bound column of the combo is a number, don't enclose it in quotes of any kind.
I guess the table in question isn't part of the form recordsource. Should it be?
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.