hi Barc777, is your question about search results on google? if so, that's a site specific preference you can set through https://www.google.com/preferences - check the setting Open each selected result in a new browser window (= a new tab in firefox) ...

I checked the setting, and saved it, but search results still open in the same window, causing me to have to go back to retrieve the page I was on.

in firefox you can also always middle-click (or hold the ctrl key while clicking) in order to open a link in a new tab.

Well, that's different. Remembering to middle-click the arrow at the end of the search field would take some getting used to, though, compared with just pressing the Enter button.

oops, i think i misunderstood your question there - if you want a new tab when you use the firefox search bar you could set that like this: enter about:config into the firefox address bar (confirm the info message in case it shows up) & search for the preference named browser.search.openintab. double-click it and change its value to true.