Your best bet is to make a child theme and simply add in the twentyten header.php with a link to your image.
How to make child theme, http://codex.wordpress.org/Child_Themes
It would be something like this ( under the branding div.)
<div id="branding" role="banner">
<div id="logo"><img src="https://wordpress.stackexchange.com/questions/5198/<?php bloginfo("template_url' ); ?>/images/YourImage.png" alt=""/></div></div><!-- #branding -->
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