Like most jQuery fx methods, .show() has a optional parameter where you can serve a callback function. The function you pass there is executed after the fx effect has finished.
$('#hidden').show('fast', function(){
$('#hideitem').hide();
});
That would pass an anonymous function as parameter, which is called after the effect. It just hides the #hideitem object then.
You'll notice that I've added an additional parameter 'fast'. That is the duration jQuery uses to execute the fadeout (can also be a number in ms). It really only makes sense to use it like this, because otherwise, .show() will just set the display property to block. Without a duration we have no delay. So a callback function for that would get invoked immediately.
If you want to show and hide that elements simultaneously just call both
$('#hidden').show();
$('#hideitem').hide();