You can announce it from both locations, but the result will be that traffic to the IP block will be delivered to whichever location provides the "best" route for the traffic, which may or may not be the site you want the traffic delivered to.
Assuming you want to split the IP block between the two locations then I see two basic approaches.
1. Speak to your ISP. See if they are prepared to announce the /24 block on your behalf and route sub-blocks of it to your two sites.
2. Establish a private link (this may be a VPN, but if it is a VPN then the VPN endpoints must not use IP addresses from the split block) between the two sites. Traffic arriving at the "wrong" site would be sent over the private link to the "right" site.