You probably wouldn't be able to tell the breed just from the colouring as lots of different breeds may show the same colour.
The colour however is called tabby point (the points - face, tail tip and ears - show tabby colouring but the body can be a solid colour as you have seen).
some breeds which are more likely to show this colouring include the british short hair, the siamese, birman, balinese. There are lots more but if you put tabby point in to google images you might see your cat!