Formula Fields not populating sum when Null values are part of formula

I am having what I believe to be a somewhat easy challenge.

I have a formula field that is calculating the sum of ten other numeric fields. This field functions correctly when all ten fields included in the formula is set to "treat blank values as 0's in calculations" and does not return any values when this is not true for any of the fields referenced in the formula.
The issue I am running into is that I need to set the trigger for "treat blank values as 0's" to not be true for these fields because they are a part of another formula field that returns values from this field or another field based on whether the values are NULL. Therefore, if the value is NULL or 0 brings back a different response in my second formula field.
Is there a way to solve this issue so that my second formula field that references the IsNull call returns the correct response but the initial formula field that is summing the ten numeric fields also returns the proper value; and generally ignores the fields that may be Null (but not have them checked to be calculated as zero).