Hello Eleanor Baker.
First try using Windows System Restore (type system restore into the Windows search box or go through the Control Panel and click on Recovery). If you can find a Restore Point dated prior to when the audio software was deleted, use that. You won't lose any of your files doing that.
It doing that is impractical or does not help, the other thing you can do is to go to the Dell support page for your model, click the Drivers button, select your 8.1 operating system, expand the Audio category, and download and install the audio driver that will be there.
Unfortunately I cannot point you directly at your support page without knowing the full model name of your laptop, but you can follow this link where there will be links to all of the Inspiron models. Find your model in the list and click its link. (Alternately you could enter your service tag number.)