Small Aircraft; Low Wing; 1 Eng; Fixed Gear
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 1
Time Pressure; Workload; Situational Awareness; Distraction; Confusion; Communication Breakdown
ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Air Traffic Control Separated Traffic; Air Traffic Control Issued Advisory / Alert
Environment - Non Weather Related; Human Factors
I was working Local Control and Tower CIC.  Aircraft Y was on final to Runway X and Aircraft X was ready to depart Runway Y.  I cleared Aircraft X for takeoff and issued a right turn heading 210.  The proper heading for the departure was 120; per LOA.  I transposed the numbers and missed my error on the readback.  After I observed Aircraft X start his turn; he began to enter a cloud layer and I switched him to departure.  A few moments later; I realized my error upon watching the radar.  I issued a traffic call to Aircraft Y on approach and he called Aircraft X in sight.  No TCAS resolution or CA alert were issued for aircraft proximity.I believe the only recommendations I could make to stop this sort of incident from occurring would be to develop Standard Instrument Departures at ZZZ; which I am not sure is feasible.  Also; I believe the COVID-19 staffing needs to be changed; and more personnel brought back to mitigate the lack of for control positions and lack of oversight.  (ZZZ is reverting to a more normal staffing schedule during Pay Period XX).
Tower Controller reported inadvertently giving an incorrect heading to a departing aircraft resulting in a conflict with an aircraft on final.