Add to sum only if it is an integer

Greetings,

I have a high vis workload planning sheet I am trying to improve.

The desired state is that the user can enter the amount of hours certain things took/will take.
The default of that cell is "Not-Entered" and color coded red if it is anything less than 0.

How would I go about making that cell not added to the total of all those cells until an integer is entered, that way the total is able to add without errors with the default "Not-Entered" still in place, and you're able to see the total of what has been entered thus far.