Tower Controller working all positions in the tower combined reported they cleared an aircraft for takeoff with another aircraft on short final and did not realize it until the arriving aircraft advised they were initiating a go around.

Narrative

I was working LC/GC/FD/TCIC (Local/Ground Control/Flight Data/Tower Controller in Charge) all combined up. Aircraft X checked in at southeast of the airport. I issued the landing clearance. 2-3 minutes had passed and the FDIO (Flight Data Input/Output) printed out three strips. I walked to the center console and grabbed the strips. As I was disseminating the information on the strips; Aircraft Y called up ready for takeoff. I looked up; scanned the runway and issued the takeoff clearance. I did not look at the TDW (Tower Display Workstation) to see who was on final. I then went back down to look at the strips as another aircraft had called ground control looking for their clearance. As Aircraft Y was rolling; Aircraft X then said 'you've got a jet on the runway'. Aircraft X then initiated their own go around. I cancelled Aircraft Y's take off clearance; issued a climb out for heading 235 climb and maintain five thousand to Aircraft X. There was also another aircraft in the left closed traffic and two other aircraft on final also cleared to land. If manning can allow; having TCIC/LC split off from GC/FD/CD. The build up from nothing going on to needing an extra pair of eyes happens too quickly. 99% of time working the tower at ZZZ can be done solo. There are few times when for safety the positions need to be de combined.