You get one energy every 4 minutes or some less. It's about 360 energy per 24h if you always keep energy not full.
Next you can work a little on your neighbors towns and get about 50 energy every 24h.
And here other ways to get energy without links.
Note for everyone. Some animals in list below can't be purchased now. And developers add new interesting energy sources every week or two. They can be removed anytime. So all below only ideas how you can get energy without links. And when you try to do this on your time, you should check market for new variants, maybe they be better than we have below.
Gold only energy sources:Edit
Horse and White horse. Give you 2 energy every 24h when you feed them. Cost 5000g and 200 oil each. You can have 10 horses and 5 white horses. You get +1 energy after feed each of them.
All 15 horses cost 75k gold and 3k oil. And give you 15 additional energy every 24h.
Other way to get energy - buy it from premium tab in shop. Best price is 20 energy for 270 supplies. Or 1 energy per 13,5 supplies. So Every livestocks who give more than this value give you a little enery for free.
Gold only supplies sources:Edit
Bufflalo and White Buffalo. Give you 80 Supplies each every 24h when you feed them. Cost 10000g and 400 oil each. You can have 10 Buffalos and 5 white buffalos. You get 66,5 free supplies or +4,9 free energy from supplies every time you feed them.
All 15 buffalos cost 150g and 6k oil. And give you about 73,8 free energy every 24h.
Gorillas. Give you 70 supplies every 24h when you feed them. Cost 800g and 300 oil each. You can have 10 gorillas. You get 56,5 free supplies or +4,1 free energy from supplies every time you feed them.
All 10 Gorillas cost 80k g and 3k oil. And give you about 41,8 free energy every 24h.
Yaks. Give you 25 Supplies each every 18h when you feed them. Cost 1500g and 80 oil each. You can have 10 Yaks. You get 11,5 free supplies or +0,85 free energy from supplies every time you feed them.
All 10 Yaks costs 15k g and 800 oil. And give you 8,5 Free energy every 18h. Or 11,3 energy every 24h.
Bank notes energy sources:Edit
You can try to find time when shop sell it with discount.
Cat. Give you 6 energy every 12h. Costs 30bn. Can have only 3. Give +5 energy after feeding.
All 3 cats costs 90 bn. And give you 15 energy every 12h or 30 energy every 24h.
Jaguars. Give you 6 energy every 12h. Costs 34bn. Can have 50. Give +5 energy after feeding.
All 50 Jaguars costs 1700bn. And give you 250 energy every 12h or 500 energy every 24h.
Goats, Mountain Goats, Seals, Panthers. Give you 4 energy every 12h. Costs 24bn each. You can get 109 this livestocks. Give you +3 energy each after feeding.
All 109 costs 2616bn. And give you 327 energy every 12h or 654 energy every 24h.
Red Magaw. Give you 2 energy every 4h. Costs 14bn each. You can have 100. Give you +1 energy each after feed.
All 100 Magaws costs 1400bn. And give you 100 energy every 4h. Or 600 energy every 24h.
Zebra. Give you 2 energy every 24h. Costs 72bn each. You can have only 10. Give you +1 energy each after feed.
All 10 Zebras costs 720bn. And give you 10 energy every 24h.