"At the time" vs "at that time"

Question

Examples:

I met Monica a year ago. At that time, I was living in New Work, in a middle-sized apartment overlooking the Mississippi River.

I met Monica a year ago. At the time, I was living in New Work, in a middle-sized apartment overlooking the Mississippi River.

Do they mean the same? Which is more appropriate for the example above?

Answer 1

In the examples you provided they basically mean the same thing. That points to the physical time a year ago, while the simply refers to the known, mentioned time, which is also a year ago. So in your case they both can be used with no difference in meaning.