One way to simplify the task would be to fill an adjacent column of the
sum range with the ABS equivalent (using abs(cell)), then use the new
column as your sum range in the SUMIF function.
If you wish to use SumIf, another option might be something like this. This
behaves a little nicer with any text or errors within the range.
=SUMIF(A1:A10,">0")-SUMIF(A1:A10,"<0")