I recently switched to PHP 7 on my development server, which has worked just fine - until now.
Since I updated to PHP 7.0.3-10+deb.sury.org~trusty+1 (ea
PHP 7.0.3-10+deb.sury.org~trusty+1
I had the same problem. Just install php7.0-xml package. Ubuntu 16.04:
php7.0-xml
sudo apt-get install php7.0-xml
Edit: Restart apache2 to load the new package.