If you change your code around a bit it works.
<div id="subpageFooter">
<div id="subpageFooterLeft">
<div style="z-index: 15; position: relative; left: 0; padding-left: 20px; padding-top: 30px; font-weight: bold; color: #00A0BE; font-size: 13px;">
Administrative Office
<img style="position: absolute; float: right; display: inline-block; left: 80%; margin-right: 15px; width: 52px; height: 51px;" src="theImages/locateit.png" title="Locate Administrative Office" alt="LocateAdministrative Office" />
</div>
<div style="z-index: 14; position: relative; left: 0; padding-left: 40px; padding-top: 10px; padding-right: 8px; font-weight: normal; color: #000000; font-size: 12px;">
1250 Avenue, Purchase, NY 36253-2547<br>
972.656.0700<br>
</div>
</div>
</div>
Working fiddle: