“Edit this” with unique serial number

Hi,

for Web Accessability Inititiave (forgive my spelling at 2 AM) purposes, I would like the link to edit each post to have that post’s number. Here is the tag I need to call with the serial number:

<?php edit_post_link('text', 'before', 'after'); ?>

I tried some foolishness like

<?php edit_post_link("Edit the_ID()", 'didn't', 'work'); ?>

Can someone please tell me how to do this? Thanks much.

Jamie