Perhaps the secret behind the trick was not explained in your reading ..
(a) consider the case where actual aircraft weight is rather less than maximum permitted for the runway and day
(b) if you use rated (ie maximum) thrust you are up and away much earlier and better than you really need
(c) if follows that you could use less thrust and still be OK so far as all the safety and regulatory considerations are concerned
(d) so how might we figure out how to use less thrust ?
(e) look up the RTOW chart at increasing OAT values until you find the same weight as your actual weight (most folks use a small pad to make the sums more conservative)
(f) what this means is that, were the actual OAT on the day equal to the higher OAT for the actual weight you have, you would be able to take off satisfactorily
(g) so, if you set that thrust (to suit the higher, assumed, OAT) you will obtain a satisfactory takeoff somewhat better than the book presumes .. due to the actual OAT's being lower than the book OAT
(h) benefit is reduced maintenance and, possibly, more favourable contract considerations/costs