Possible solution:
Float the Search Field's parent container to the left. Possible CSS follows:
.searchContainerClassName {float:left; width:yourSearchContainerWidth;}
Then float the Results area's parent container to the right. Finally, change the width of the Results area's parent container so that it equals the difference between the Search Field's parent container and the page width (ie. Search Field container width minus page width = Results are container width). Possible CSS follows:
.resultsContainerClassName {float:right; width:yourResultsContainerWidth;}
This is one approach. Note: floats can be a tricky endeavor.