Beautiful floors. I suggest you contact a professional flooring contractor. Real estate agents often have referrals. Some close up photos with a coin and a ruler for scale would be useful to take with you when initially talking to a flooring contractor in the shop. Include a piece of white paper to show colors better.

You can purchase unfinished wood flooring, and have both floors stained to the same color, then sealed, to help blend them.

My first thought is Birch. Photos don't do justice, best bet would be to contact a local flooring company (not a big box store like home depot or lowes) and have someone come out and look at the product first hand.

I would recommend what sooz001 said which is to purchase unfinished flooring and stain both rooms to be the same color and finish. The floor is most likely birch or maple.

Otherwise, you are better off to purchase a different color and/or species of wood so it does not appear that you tried to match the floor and didn't quite do it.

The last option is where the new floor and existing floor touch, remove some of the existing floor and weave in the new floor to the existing so it is not a straight line of different flooring. This does require to you have the same thickness of floor and width.

Best of luck on your wood floors!