TYPO3 uses external software called "diff" for creating a coloured view of the difference. Have a look at t3lib/class.t3lib_diff.php for implementation details.
I guess $GLOBALS['TYPO3_CONF_VARS']['BE']['diff_path'] is set wrong or diff is not available.
untested:
If you cannot ask the admin of your server, create an php-file somehow like this for testing purpose:
<?php
$GLOBALS['TYPO3_CONF_VARS']['BE']['diff_path'] = '/usr/bin/'; // do not know your system
$file1 = '';
$file2 = '';
$cmd = $GLOBALS['TYPO3_CONF_VARS']['BE']['diff_path'] . ' ' . $file1 . ' ' . $file2;
$res = array();
echo exec($cmd, $res, $returnValue)
echo $res;
?>
This file should output something like
diff: missing operand