Currently, "Enhancement Cores" are achievable by Banshee's and Clan Bounties, Legend Nightfall or Legend/Master Lost Sectors.
The Problem is, these sources are not giving enough to fullfill day to day weapon masterwork requirements. At least for me as a new player.
I think it would be better if the quantity of Enhancement Cores from all these activites are just get doubled. Or just give some option to trade Enhancement Prism for Cores. I always have more Prism than Cores even sometimes Cores get below Ascendant Shards. Please Bungie, just take 1 Ascendant Shard and give me 50 cores if possible.
I think everyone would've faced this problem once and doubling the Core drops will make things easier.
They can also drop when anytime you get a legendary piece of gear or dismantle a legendary weapon.
If you are still sitting on a pile of Vanguard tokens, I highly suggest cashing those in before Tuesday.