“It’s called Cross Sums in the USA, Kakuro in the UK, and Kakro in Japan.”.
(from kakuropuzzle.com)

“Works as crosswords, but the givens are substituted with sums.
You can use numbers from 1 to 9.”.
(Vegard Hanssen from menneske.no)

“Kakuro has clues both across and down.
When you put numbers in the vacant squares, the sum must equal the given clues.
Just like a sudoku, you cannot have the same number in a row or column.”.
(from kakuro.cc)