"Dogs are not our whole lives, but they help make our lives whole."
-Roger Caras

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Separation anxiety is a fairly-common problem. Many dog trainers have tips that they have found to help a lot of dogs. Some cases are really bad, but some are fairly easily helped with a few weeks of work.  

How do you fix separation anxiety? Can you train a dog to not bark or be worried when you leave home? Yes, it can be done with many/most dogs, though training or even with some helpful medicines if those become necessary (see your veterinarian about that latter option).

Since I am not an expert on this topic, and am just collecting some information that seems quite helpful, I will refer you to some promising links rather than typing a lot of possibly-incorrect information here.

This one has lots of tips: http://www.dog-obedience-training-review.com/separation-anxiety-in-dogs.html

Caesar usually has some very tried-and-true tips: https://www.cesarsway.com/dog-behavior/anxiety/leaving-your-dog-home-alone 

Kind of similar: http://www.aspca.org/pet-care/virtual-pet-behaviorist/dog-behavior/separation-anxiety 

This one centers on a theory that it is worse if the dog doesn't see YOU as the alpha dog, which is interesting: http://www.dogbreedinfo.com/separationanxiety.htm 

I don't know if you have tried one of these, but several people have told me they are wonderful! Thunder Shirts: http://www.thundershirt.com/ 

Tips in general: https://woofwhiskers.com/best-anxiety-reducers-dogs/

What about getting a second dog?

It seems the easiest solution. If separation anxiety is caused partially by a pack/leadership issue, a second dog seems like it would solve the problem.

True...it may seem the easiest solution "for your dog." But will it work for your family to have a second dog? Will two dogs simply learn poor behavior from each other, rather than settling each other and creating a happier environment when you are away from home? That's a guess, and a risk, of getting a second dog.

If it may be a bit of a stretch spending time with two dogs instead of one, please try other ideas for a workable solution before jumping after a second dog. :-)