How do we make slam?

You didn’t tell me who opened so I’m going to assume it was the person (I’ll call North) with the 18-point hand as I can’t imagine that if South opened 1NT that you would have missed a Slam.

So, here is my suggested bidding:

North              South

1D                   1H

2N                   4C

4S                    6N

South has no reason to be in a hurry to show his HCPs since a new suit by Responder is forcing. South should simply bid his four-card major at the one-level. North then will jump to 2NT to show 18-19 HCPs.

South has 17-HCPs. Even though the rule is that you should not ask for Aces if you have two quick losers in a suit, [South does not hold the ♠A or K] there are exceptions. This hand is one of them.

Gerber is acceptable because it is impossible for you to be off an AK. In this hand, South knows that he and partner have a minimum of 35-HCPs between the two hands. You cannot be missing an AK because that would total 7-HCPs.That’s impossible since only 5-HCPs missing.

4♣ is Gerber asks for Aces. 4♠ shows two Aces. You are missing one Ace, so only bid 6NT.