Search Table, Display Column Header

Assuming that you will get an exact match in your row headers and in your table (otherwise you can build a lot of IF functions into this);
Setting A1 to your row header you are looking for
B1 to your table entry you are looking for
B2:I2 is column headers (final answer)
A3:A32 is your row headers

=INDEX($B$2:$I$2,1,MATCH($B$1,OFFSET($B$2:$I$2,MATCH($A$1,$A$3:$A$32,0),0),0))

See attachment below.

Edit: The OFFSET function is volatile so this may slow down your calculations if your spreadsheet is complex. DONKEY OTE is the master of replacing volatile Functions but I don't see how this one would easily be replaced. He might know.

Hey, I only just ran a quick search to see if I'd been slated anywhere (I wasn't already aware of!) and came across this and yes you could avoid OFFSET here by using INDEX in such a way as to return all columns for a given row... ie this:

=INDEX($B$2:$I$2,1,MATCH($B$1,OFFSET($B$2:$I$2,MATCH($A$1,$A$3:$A$32,0),0),0))

could become

=INDEX($B$2:$I$2,MATCH($B$1,INDEX($B$3:$I$32,MATCH($A$1,$A$3:$A$32,0),0),0))

So you run the MATCH of value against a range generated by the INDEX which itself is determined by the MATCH of value 1 against the left hand side column - by setting the column to 0 in the INDEX the range returns all values in that row (ie all columns)... because the final range is a Vector (1 row) you don't actually need to specify both column & row flag you need only specify that which is variable
(ie for a vertical vector column will always be 1 and for a horizontal vector the opposite is true in so far as the Row will always be 1)

EDIT: P.S. Flattery gets you everywhere... I don't think I've been referred to as the Master of anything other than of perhaps "disaster"...

Thanks DO!
Filing that formula away for future reference.