No, it's not possible without extra information. Just think: if the house was 20 feet tall and 100 feet away, you couldn't distinguish that from the case where the house was 30 feet tall and 150 feet away. Those two would lead to exactly the same image.
Here are some possible options you could consider:
If you have two pictures of the same house taken from two different positions, and you know the relative positions (e.g., one was 10 feet to the right of the other), then you may be able to infer the distance to the house, using parallax.
If you know the height of some feature in the image -- say, the door -- and you know all of the camera parameters (in particular, the angular resolution of a single pixel or of the field of view), then you can work out the distance to the house. So if you could calibrate the camera in advance, and make a guess/assumption about the height of the door, you could draw an inference about the distance to the house.
However this does require knowing all the camera parameters, which will probably require some calibration; I just knowing the image format, resolution, etc. and the camera resolution etc. will not be enough, and even knowing the model of the camera will probably not be enough. (Possibly if you knew the exact model of the camera and could go buy another camera of the same model, you might be able to calibrate the second one and assume both cameras have the same calibration. I don't know if that would work.)
See also Using Headpose Vector and 2D Points to Compute Distances. You might also look into camera intrinsics, camera extrinsics, the pinhole camera, and similar topics from computer graphics / computer vision.