Let us give thanks, as this holiday season begins, that at least one of the vexing problems confronting us is moving toward solution in 1983. Next year should be the year that the Social Security issue, of which so much was heard in the recent election campaign, gets resolved.

No issue has aroused more disquiet and distemper in our society. The fears of the elderly and of those nearing retirement age have been aroused and exploited, and politicians of both parties have accused each other of manipulating those concerns for selfish purposes.

The trust funds backing up the pension, disability and health-care payments have been depleted to the point of danger. At long last, the politicians have acknowledged that no longer can they delay the day of reckoning.

Fortunately, Social Security is a solvable problem. It is not like nuclear arms control, the reinvigoration of the economy or the restoration of America's competitive position in the world. Those issues all pose intellectual challenges of infinite complexity. And they confound the optimists with the realization that even if the "correct" policy is adopted, people and events beyond our control may thwart the chances of success.

In Social Security, by contrast, we are dealing with a measurable, finite problem, and there are a variety of means available for solving it -- once the political conditions permit a solution.

The National Commission on Social Security Reform has agreed that between 1983 and 1989 we must close a gap of $150 billion to $200 billion between projected Social Security taxes and outlays.

That sounds like a lot, and it is. But so vast is the scale of this social insurance system that relatively minor tax and benefit adjustments can produce the needed dollar amounts. For example, the commission calculated that the system can be kept solvent for the next 75 years by benefit cuts or tax increases totaling less than 2 percent of the wages to be earned in that period.

All that stands in the way of solving the Social Security problem is a political agreement between the Republican president and the Democratic speaker of the House that now is the time to solve it. Ronald Reagan and Tip O'Neill have every reason to make such an agreement.

Reagan has been burned repeatedly on the issue--and certainly wants it out of the way before the 1984 election. O'Neill, it seems, has reasons of his own for feeling the same way. Earlier this month, a close associate of the speaker told me, "This could well be Tip's last Congress coming up. He wants to go into the history books as the man who saved Social Security for future generations, not let it go bankrupt."

If true, that represents a crucial change of heart. Eighteen months ago, Reagan's initial misstep in calling for an abrupt reduction in benefits for early retirees showed the beleaguered Democratic leader that Social Security might be the answer to his party's political prayers. O'Neill intervened bluntly and publicly to prevent a Social Security bill from being brought to the floor of the House. At that point, he wanted an issue--not a solution.

But now the signals have changed. House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) has announced that Social Security hearings will begin this winter, with the goal of taking a bill to the floor by spring. Rostenkowski would not make that announcement without O'Neill's approval.

But will the rank and file go along with any bill that raises Social Security taxes or cuts future benefits? I asked that question of Rep. Tony Coelho, the chairman of the Democratic Congressional Campaign Committee. He said that even the big freshman Democratic class, many of whom gained their victories on the Social Security issue, will accept the bill Rostenkowski brings forward, so long as it is blessed by Rep. Claude Pepper (D-Fla.).

The 82-year-old Pepper has become the Democrats' Social Security guru, appearing in person and on film in dozens of Democratic campaigns. Last week, Pepper put himself in a strategic position by shifting from the chairmanship of the Special Committee on the Aging to the soon-to-be-vacated chairmanship of the House Rules Committee, the last stop for the Social Security bill (and most other legislation) before it reaches the floor. Any Social Security bill that comes to the floor will bear his blessing.

There are still likely to be some sharp philosophical and partisan disputes about the mixture of tax hikes, benefit cuts or caps, eligibility changes and retirement-age adjustments that may best fill the 2 percent gap.

Those issues are important. But the good news is that the House Democrats have signaled their readiness to accept their legislative responsibility on this issue--and that the issue itself presents no insoluble problems.

That's more than you can say about most of our other problems.