how to create a substraction matrix (subtract a row of every column from the same row in other columns)

I want to create a matrix similar to a correlation matrix, but with the
difference between the two values, like this

x1   x2         x3         x4          x5
x1   x2-x1    x3-x1     x4-x1     x5-x1
x2               x3-x2     x4-x2     x5-x2
x3                           x4-x3      x5-x3
x4                                        x5-x4
x5

Then I want to convert it back to a data frame with a column that describes
what columns were used in the calculation, but I would like to only include
the comparisons that go forward in number. Basically, each number represents
a year, and I want each comparison to only be listed once, the difference
between the 1st year the sample was taken and then 2nd year the sample was
taken. (This would probably entail just taking a portion of the matrix.) .