Do I plug the 20 Pin AND the 10 Pin into my PSU?

I think you're confused. The deluxe has a 24-pin connection and an 8-pin connection. The PSU should have a 4-pin piece on the same length of cable as the 20-pin plug and should have a 4-pin with an additional 4-pin plug done the same way as the 20+4. it's a modular PSU so check through your cables and make sure you have the right ones plugged in. both the 20+4 and the 4+4 need to be plugged into the mobo for adequate and stable power.

hope that helps.

Yeah, I see that my motherboard has the 24 pin and 8 pin connection.

The 24 pin connection has two connectors on the other end; a 20 pin and a 10 pin (no 4 pin connector on the same end as the 24 pin). This is what I'm most confused about. The 20 pin and the 10 pin also can't be plugged in more than a couple of inches apart which is why I'm pretty sure they both go into the PSU, so am mostly just asking if I need to plug in the 10 pin as the PSU documentation makes no mention of it.

The 8 pin connector has 2 x 4 pin connectors on the other end. The 4+4 needs to be plugged into the EATX12V on the motherboard, and the 8 pin into the PSU?

if those are the only connections on that cable, then yes. I'm honestly not familiar with that PSU so I can't help much more than I have. Are you sure there's not a +4 tied back or something on that 20-pin? or a 24-pin variant in the box?

Edit: looking on corsair's webpage, the 4+4 hooks up just like you assumed and the atx connector should be 24-pin. I'm looking at a picture of i now and it shows 24-pins, not 20.