I need to find the largest, second largest, etc numbers across a set in a
row then have the formula return the columns header (different row, same
column).

I put header values in A1:J1, and numbers in A2:J14.

I put formulas to show the headers for the largest number of each row in K2:K14; second largest, L2:L14, etc.

The formulas started with this in K2:
=INDEX($A$1:$J$1,1,MATCH(LARGE($A2:$J2,COLUMN()-10),$A2:$J2,0))
Then copy the formula to all of K2:T14.

Modify to conform wiuth your data layout.

Hope this helps getting started.