Why can I ping 10.0.0.0/8 addresses from a 192.168.1.0/24 subnet?

I thought 10.0.0.0/8 were all reserved addresses and that any sort of traffic going to those addresses was dropped.

No. It's true that it's a special range, but it's reserved for exactly the same purpose as 192.168.0.0/16 – it is a private address block for LAN usage. (There is also a third block, 172.16.0.0/12. See the IANA registry.)

All three private blocks act as normal unicast addresses and are routable locally, including between each other – they're just not routable across the global Internet. (What's actually dropped is traffic and route announcements between ISPs.)

So most likely you're pinging some host in your ISP's network, where they've decided to use 10.0.0.0/8. It could be a device on their internal network, or a 'management' VLAN on your router itself, or anything.

These are three most likely possibilities:

1. Your ISP assigns its clients the 10.0.0.0/8 addresses. Your home router isn't advanced enough (nor needs to be) to limit routing private blocks upwards.

2. You have an additional routing device between your router and ISP, like a cable modem, which communicates with your router over 10.0.0.0/8.

3. You host or access 10.0.0.0/8 network directly at your computer (i.e., a virtual machine network or some VPN).

The most important question is: why do you ping 10.10.10.140 specifically? Also, trying to access popular management services (HTTP, HTTPS, SSH, and Telnet) might reveal device identity and purpose.

You potentially could have a device on the network using that IP address that you are not aware of. The 10/8 range is not routable over the internet. I would take a look at your routes and see where its going.