for example, I have 2 columns of data:
3 6
4 2
1 1
7 3

I want to RANK the sum of each row but do not want to store the sum in
another column first.

the sums a
9
6
2
10

so in column C, I want to see
3
2
1
4

Resulting sheet would look like:
3 6 3
4 2 2
1 1 1
7 3 4

I tried this for the formula in C and it did not like it ($ present to make
it easy for fill down):
=RANK(a1+b1,($a$1+$b$1):($a$4+$b$4),1)

I tried SHIFT+CTRL+ENTER thinking it might be an array formula but that did
not work either.

Again, the crux of my dilemma is that I do not want to store the sum in
another column prior to ranking.