The example of E_ALL ^ E_NOTICE is a 'bit' confusing for those of us not wholly conversant with bitwise operators.
If you wish to remove notices from the current level, whatever that unknown level might be, use & ~ instead:
<?php
$errorlevel=error_reporting();
error_reporting($errorlevel & ~E_NOTICE);
error_reporting($errorlevel);
?>
^ is the xor (bit flipping) operator and would actually turn notices *on* if they were previously off (in the error level on its left). It works in the example because E_ALL is guaranteed to have the bit for E_NOTICE set, so when ^ flips that bit, it is in fact turned off. & ~ (and not) will always turn off the bits specified by the right-hand parameter, whether or not they were on or off.