We have been able to conditionally sum a column of cells (sum_range) based
on the blank cells in another column (range) using
SUMIF(A$8:A20,"",B$8:B20). Nevertheless, we actually need to sum the
NON-BLANK cells in the sum_range column. How do we create a formula that
will sum the non-blank cells?

Please note that we have tried several iterations of the formula 'criteria'
argument including NOT(""), NOT(""""), "NOT("")", "NOT("""")", ISBLANK(),
"ISBLANK()", and so forth. We have most likely failed to understand the
proper syntax for the 'criteria' argument, but there surely must be a
criteria that will identify the non-blank cells, isn't there? Currently, we
are subtracting the sumif result, for the blank cell criteria, from the
total of the column in order to find the difference. Unfortunately, this is
a temporary and cumbersome work-around. We thank you for any help with this
issue.