
I want to be able to position the div (element E) inside the TD cell (element C) without the other TD cell (element D) getting pushed to the right.
Note: I can't edit anything on that page except for element E.
Since you cannot edit any other element except for element E itself:
Move element E to a container:
<div style="position:relative;">
<div id="element-E" style="position:absolute;"> ... </div>
</div>
I've added style attributes to the elements, because you alleged to not be able to modify other elements (such as <style>).
position:relative is required to correctly absolutely position a child element.
position:absolute; "tears" the element from its parent, and places it back again, relative to the upper-left corner of the parent (by default, when the position hasn't changed using top for example).
Negative right margin ought to do the trick: margin-right: -50px;.
example: http://jsfiddle.net/peteorpeter/dvr9Z/
Absolute position could work, but adds other complications. Tables + absolute position can be painful, especially with fluid content.
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