Blank cell formula

If you don't want to use conditional formatting (which would be good choice) then you can do something like this:

=IF(SUM(B2:E2)=0,"",SUM(B2:E2))

If your region uses , as a decimal separator the formula would be:

=IF(SUM(B2:E2)=0;"";SUM(B2:E2))

SG

If you want to use conditional formatting, make a different custom format than that. You can to set the opacity of the text to zero, which makes it disappear regardless of background color. In the screenshot below I clicked on the little color wheel where you pick the text color. The color wheel window pops up and you can drag the opacity slider to zero. The table has zeros in column B but you cannot see any of them.

The reason the formulas are longer is because you have "use header names as labels" turned on in Numbers/Preferences. I find it makes the formulas harder to read so I never use that feature.

The reason your formula fails is the negative signs. Your formulas for F2 and M2 result in either a number or a null string. The double quotes with nothing between them creates a null string which is a string with no characters in it. You can take a negative of a number but you cannot take a negative of a string, not even of a null string. Your formula is trying to take a negative of cell F2 but F2 is a null string.

Personally, I think your earlier solution of hiding the zeros might be the better idea than these formulas that are much more complicated than necessary. Forget about checking for zero and setting to a null string if it is, just do the proper math and if it is zero it will be zero. I think I would hide the zeros with a custom format, not a conditional format. Instead of setting the opacity to zero when the result is zero, create a custom format that shows nothing when the result is zero. Choose "create custom format" as the data format for the cell. Add a rule that shows nothing when equal to zero. Edit the other rule to show what you want to see otherwise. Give it a descriptive name. You can use that new format for all the other cells that need it. If you edit it later for some reason, the edits will apply to all cells which use it. Below is an example for currency. I am doing this on a Mac, not an iPad.

It is my opinion you are digging the hole deeper. But, to answer your question, replacing the first

-'Expenses Total ' 'Wed, 1 Apr 2020'

with

-SUM('Expenses Total ' 'Wed, 1 Apr 2020', 0)

should make it work. I don't think the second one requires it.

You can see how much this is complicating your formulas. The method you are using is appropriate for a lot of things but, in my opinion, not for what you are doing. You need three SUMS and an IF where you should have a single SUM. Instead of =SUM(M2-F2) you have =IF(SUM(M2-SUM(F2,0))=0,"",SUM(M2-F2)). That is so much more complicated, harder to read, and harder to debug to uncover a mistake.

Also, you would not need to use SUM at all if the cells you are adding or subtracting are actual numbers, not null strings. A simple + or - will do the job if the cells are not strings.

=M2-F2 is the same as =SUM(M2,-F2)

It is simpler, shorter, and quicker to type.

I do not see an option to turn off header names as labels in the iOS version.

My apologies. My mistake when typing the formula. I left out the commas in the SUM functions.

=IF(SUM(M2,-SUM(F2,0))=0,"",SUM(M2,-F2))

Looks like we have to do the same to the last part of the formula that we did to the first. Digging that hole a little deeper.

=IF(SUM(M2,-SUM(F2,0))=0,"",SUM(M2,-SUM(F2,0)))