The right div with a fixed width must float:right; then the left div must stay as it is so it can take its full available width, but since you want the right div to be fixed, you must place it first.
HTML:
<div id="parentDiv">
<div id="rightFixedDiv"></div>
<div id="leftDynamicDiv></div>
</div>
CSS:
#rightFixedDiv
{
float:right;
border-style:solid;
width:100px;
height:200px;
}
#leftDynamicDiv
{
border-style:solid;
background-color:blue;
overflow:hidden;
height:200px;
}
Check it out, fixed width of 100px: http://jsfiddle.net/dkGbd/
fixed width of 200px: http://jsfiddle.net/eESTZ/
Now if you want the opposite, place the left div first, give it a float:left;
Working example:
http://jsfiddle.net/UShek/