If you've not played much or any of the game, maybe look away from this guide as it's gonna spoil the game a somewhat for you. Having said that, let's continue.
Quantum Essences are something you will start to see as you progress the game a bit. They will be dropped by an enemy called the Starborn. Now I'm gonna list the ways which I encountered the Starborn by don't worry, I finished the game with 25 having using 2 so collected 27 in total so get the required 20 shouldn't be a massive issue, I also didn't find every temple either. If you want to check how many you have, pause the game, press up and A so now you're in the power screen and look at the bottom left.
First the temples, these are the things you later get powers from, everytime you complete 1 a Starborn will appear after, kill him and you'll get an essence. Keep in mind, their bodies disintegrate, you won't be able to search them you are just given the essence.
Second the story and I'm gonna spoil a later mission for you so look away if you've not finished or very close to finishing a play through. Once you meet the Hunter and Emissary, you'll be sent to the Moon to search through NASA after getting the artefact the Starborn will attack on you way up. You'll likely get 5-10 this way, which is a good method. The final mission will also have more Starborn, however for me, not every Starborn here dropped one, I got one after completing each battle section which gave me around an extra 5/6 in total.
Third, once all artefacts were collected they task you with putting them in the armillary and grav jumping somewhere. At this point I chose to rack up the rest of my achievements and having the armillary on your ship makes you a target. You'll randomly see Starborn craft land on a planet, go to it because about 5 Starborn will get out every time and are good source of Essence.
Fourth and this one I haven't tested so I'm completely guessing. You can put the armillary at an outpost which will make that outpost a target for the Starborn. I would imagine this would also work by defending it, so I'm putting it here just in case.
I will warn though, my Essences did not carry over into new game plus, so if you're planning to get 10 and 10 in different playthroughs, don't. Get it in 1 playthrough, it shouldn't be too difficult and good luck.