Teaser 2821: Magic cards

From The Sunday Times, 16th October 2016 [link]

 Joe placed nine cards on the table to form the magic square shown on the left below (where each row, column and diagonal has the same total). Then he turned over each card one at a time and the result is shown on the right below: it is not magic.

Penny then rearranged the cards to form a magic square which, after each card was turned over, was also magic.

What (in increasing order) were the four corner numbers in her magic square with the higher total?

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