Sorry, I'm not good at explaining things in words but I'll try. If this still doesn't come clear, sorry, I just woke up

The op amps inside the head can swing its output to the plus or minus voltage minus 2V. Since the output is ground referenced (brown wire) you can only go to the plus or minus voltage. If you're using two 9V batteries, that would be plus 9V or minus 9V. Subtract the 2V dropout of the op amp's output stage, you get 7V maximum output swing.

Now, you're planning to use a 36V supply, which you will then split in two to get plus and minus 18V. So now the ophir output will be referenced to the new "ground" which is the midway or the "split" which is at the middle of that 36V supply. So now the op amps have plus and minus 18V supplies. With zero input, your output will be at the midpoint or split of the 36V. So you have 18V minus the dropout which results to 16V swing. To have a 20V output, you'd need plus and minus 22V rails or 44V total which is well beyond the max supply voltage for the op amps.

The 20W rating mentioned is for the 20CA-0.1-Y which has an 0.1V output per 1 watt input which would only need a 2V swing for 20W input. I'll try to dig up where I read it and link it here.