Outlet Wiring Identification
You'll want a few extra parts for this

The wiring runs in this box appear to have been made using new-style armored cable (AC) that has a bonding strip in it, which means that you don't have a ground wire; instead, the combination of the cable armor and bonding strip serves as the grounding path.  As a result, you'll either need to return your receptacle and get one with a self-grounding feature (in addition to tamper-resistance, that is!), or get a ground pigtail that you can screw into the designated grounding hole in the back of the box to provide a ground wire to the receptacle's grounding screw.  (You also may need to return the receptacle anyway, since it won't fit the existing faceplate as it's decorator-style (big rectangular opening) vs using a standard (two roundish openings) receptacle opening on a faceplate.)

While you're there, get a short length (3-6") of black 12AWG THHN and a wirenut suitable for three 12AWG wires.  Once you return with the right things, you'll then need to strip the insulation off the ends of the black wire you bought, and use the wirenut to combine it with the existing black and red wires in the box -- crank it down tight and make sure it passes a pull test!  Then, you can install the ground pigtail and wire it to the green screw on the new receptacle if you went that route.  Once that's done, the black pigtail goes to the brass screw and the existing (yellowish) white pigtail goes to the silver screw on the receptacle; once the receptacle's all wired up, you can button things back up, turn the power back on, and enjoy your work!