throws Exception in finally blocks

Is there an elegant way to handle exceptions that are thrown in finally block?

For example:

try {
  // Use the resource.
}
catch( Exception ex ) {
  // Problem with the resource.
}
finally {
   try{
     resource.close();
   }
   catch( Exception ex ) {
     // Could not close the resource?
   }
}

How do you avoid the try/catch in the finally block?