Sort and Re-apply Deltas of an Array

MATL, 8 bytes

1)GdShYs

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1)   % Implicit input. Get its first entry
G    % Push input again
d    % Differences
S    % Sort
h    % Concatenate
Ys   % Cumulative sum. Implicit display

Jelly, 7 bytes

IṢ;@Ḣ+\

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How it works

IṢ;@Ḣ+\  Main link. Argument: A (array)

I        Increments; compute the deltas.
 Ṣ       Sort them.
    Ḣ    Head; pop and yield the first element of A.
  ;@     Concatenate with swapped arguments.
     +\  Take the cumulative sum.

Mathematica, 40 bytes

FoldList[Plus,#&@@#,Sort@Differences@#]&

Pure function taking a list of (anythings) as input and returning a list. FoldList[Plus starts with a number (in this case, #&@@#, the first element of the input) and repeatedly adds elements of the self-explanatory list Sort@Differences@#. This mimics the behavior of the built-in Accumulate, but the first number would need to be prepended to the list of differences by hand, which makes the byte-count higher (as far as I can tell).