You said that East should play the King. You are correct.He knows that the Ace has gone, and that the Queen is in the Dummy, but not involved in this trick, but he doesn't know where the Jack is. He takes the trick, rather than hoping that his partner might win it.
So the trick continues, with Declarer playing the 2, and West playing the 8.
Now East has won the second trick of their partnership. These are the cards that he has left. Between him and his partner they should win the rest. It doesn't really matter which order they are played in.
Spades 10
Hearts
Diamonds 5
Clubs 10
Let's have East play his boss Ten of Clubs first.
Declarer plays the 8
West plays the Jack of Spades
Dummy plays the 2 of Clubs
Then East plays the 5 of Diamonds, knowing that his partner
still has the Ace in that suit.
Declarer plays the 5 of Spades
West plays the Ace of Diamonds
Dummy plays the Jack of Diamonds
West now plays the Ten of Diamonds
Dummy plays the Queen of Spades
West plays the Ten of Spades
Declarer plays the 9 of Spades
The end result is that North and South have won 8 tricks, and East and West have won 5.
22. How many points will North and South score towards their game?