Template administration Error after WP 4.8 update

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This is a generic PHP question, but simple to answer. The problem is most likely caused by PHP 7.

Simply change the line:

$callback[0]->$callback[1]();

to

$callback[0]->{$callback[1]}();

This is because $callback[0]->$callback[1](); means $callback[0]->{$callback[1]}(); in PHP5, while it means ($callback[0]->$callback)[1](); in PHP7.

Take a look into this page to know the details about the change.