TableForm[Table[{x + y, x - y}, {x, 10}, {y, 10}], TableHeadings -> {Table[x, {x, 10}], Table[y, {y, 10}]}]

Grid[{
      {" ", "x y", Sequence @@ Table[x, {x, 10}]},
      Sequence @@ MapThread[Prepend /* Flatten,
                 {
                  Table[Column[{x + y, x - y}], {x, 10}, {y, 10}],
                  Table[{Column[{"x+y", "x-y"}], x}, {x, 10}]
                 }]
      },
    Dividers -> {{2 -> True, 3 -> True}, 2 -> True}]

TableForm[Table[
{x + y, x - y}, {x, 5}, {y, 5}],
 TableHeadings -> {Table[x, {x, 10}], Table[y, {y, 10}],{x+y,x-y}}]

fileName=CreateTemporary[];
st=OpenWrite[fileName,FormatType-> OutputForm];
Write[st,TableForm[
 Table[{x + y, x - y}, {x, 5}, {y, 5}],
 TableHeadings -> {Table[x, {x, 5}], Table[y, {y, 5}],{x+y,x-y}},
 TableAlignments-> {Right,Top,Right}],
 ];
Close[st];
Import[fileName]

ToString@Format[TableForm[
Table[{x+y,x-y},{x,5},{y,5}],
Table‌​Headings->{Table[x,{‌​x,5}],Table[y,{y,5}]‌​,{x+y,x-y}},
TableAli‌​gnments->{Right,Top,‌​Right}],OutputForm]

flatTableForm[Table[{x + y, x - y}, {x, 10}, {y, 10}],
 TableHeadings -> {Table[x, {x, 10}],
   Table[y, {y, 10}], {x + y, x - y}}]