Help identifying a SOP-18 IC (labels removed) by reverse engineered circuit
2 pins coming from an MCU sounds like a serial link; since the IC has 10 parallel outputs, this smells like a serial to parallel shift register.

The 10kΩ resistor is probably used to set the current that the IC allows each LED to sink into Pin 1–3, 6–10, 17–18.

This sounds like one of the relatively popular LED drivers out there; for example, starchip SCT2016, though that has 16 output channels.

The fact that there's no marking on the package might mean you simply can't buy that chip: might be a one-off run in some old wafer fab.

If the marking was actually scraped off: this surely hasn't happened because someone tried to hide trade secrets from their competitors (this LED driver's job is so obvious that this wouldn't help, at all), but probably because these are counterfeits of some large IC manufacturer's design and they couldn't have imported the device with the counterfeits claiming they were the real deal.

I tried to look through the LED drivers over at octoparts.com and filtered for ICs with 18 pins – link – but none of these even remotely have a comparable pinout to yours. Since Octopart only list major distributor inventory (ie. none of the "small chinese company with 2 engineers that runs wafers on the cheapest technology that written-off wafer fabs offer"), it's pretty unlikely you'll be able to find a chip that's 100% compatible to yours.