Strangely enough you can 'almost' do this with list(), but you can't use it in a function call. I only post it as you say 'more out of interest' :-
$_GET['unique'] = "blahblahblah=this_is_what_im_interested_in";
list(, $second) = explode('=', $_GET['unique']);
var_dump($second);
Output:-
string 'this_is_what_im_interested_in' (length=29)
You can see good examples of how flexible list() is in the first set of examples on the manual page.
I think it is worth pointing out that although your example will work:-
$common->resetPasswordReply(explode('=', $_GET['unique'])[1]);
it does kind of obfuscate your code and it is not obvious what you are passing into the function. Whereas something like the following is much more readable:-
list(, $replyText) = explode('=', $_GET['unique']);
$common->resetPasswordReply($replyText));
Think about coming back to your code in 6 months time and trying to debug it. Make it as self documenting as possible. Also, don't forget that, as you are taking user input here, it will need to be sanitised at some point.