Replace breaker with Tandem
All we can see is QP and hom breakers  we need to see the texts printed on the panel to provide help. The breakers need to be listed for the panel. , since this information is lacking a code compliant recommendation is impossible. Square D panel has Non CTL breakers and double stuff breakers but we need to know the type of panel to suggest a code compliant breaker. 

Added with the panel photo;
 that is a 40-40 panel so you can not use double stuff or cheaters. The proper path forward would to be to add a sub panel to the side. Remove 2 breakers from that panel and use those slots to install a feeder breaker to your sub. The wires for those 2 breakers including the neutrals and ground can be pigtailed or spliced and pulled into the sub then hooked back up. You will need a 4 wire feeder 2 hot 1 neutral and 1 ground to the new sub panel. The ground and neutral need to be isolated so if your new panel has a bonding screw or copper jumper that would need to be removed. This is the only code compliant way to proceed with that panel.