HAVING EAGERLY promised to solve the state's most serious social and financial problems, Congressman Robert L. Ehrlich Jr., Maryland's next governor, will have little time to savor a well-earned victory. Now begins what is usually referred to as the period of transition, a term too abstract to convey its importance for a newly elected governor who must begin to operate almost immediately as if the inauguration has already occurred. There's no time to wait.

These transition weeks are critically important - and doubly so this year. Mr. Ehrlich's administration will begin its talent search, moving quickly to fill Cabinet posts or to leave some Cabinet secretaries in place. The selections must be done carefully and quickly, two conflicting requirements.

But the process must go well because it will set the tone for the next four years - and help determine whether Mr. Ehrlich will succeed or fail. In some ways, the current administration in Annapolis still suffers for stumbles made during its first months in office.

He takes over in a time of real challenge.

Maryland faces a projected budget deficit of at least $1.7 billion, a daunting figure that demands immediate action. Pressures to spend on education, public safety and health care almost certainly will grow - and they will be legitimate. A new governor must pay the bills, of course. But the needs of the state must not be set aside.

Mr. Ehrlich will face harder decisions than a candidate would have eagerly endorsed. Deep resolve, honest talk to the people of the state and political skills of a kind untested until now will be needed immediately.

Mr. Ehrlich, Gov. Parris N. Glendening and State House leaders should meet as quickly as possible to discuss how to address the yawning financial gap. Maryland can't wait for rescue by a sputtering economy. Mr. Glendening has imposed a hard freeze on hiring, but more stringent action probably will be needed to avoid damage to people and programs. Whether the budget can be balanced without major retrenchment seems unlikely - campaign promises to the contrary notwithstanding. Others - not involved in a race for votes - have said virtually every area of spending must be on the table. Plenty of expertise can be marshaled to address this problem, and that must surely be Job One.

The new Republican governor must bring leaders of differing philosophies together in an atmosphere of joint problem-solving. It won't be easy. But the task does not fall to the new administration alone. Each of the state's elected leaders will have an obligation as a public servant to work with the new executive, recognizing that the price of disharmony will be harm to Marylanders. The time for pure politics ended yesterday.

In an election as closely fought as this one, neither side could have claimed complete victory. Both candidates offered good ideas and sketched out promising new directions. The momentum of higher education, pushing Maryland universities to a high level of respect nationally, must be preserved. The health care concerns of Marylanders and programs already in place to widen insurance coverage must be maintained if possible. Elements of the criminal justice system demand immediate attention. The pace will be unremitting - but a new executive could thrive on it with the right team. That is the challenge of the transition.

And if all of these tasks were not enough to consume every waking hour of the new governor, equally demanding though less tangible work must be considered. This election showed real divisions between suburb and city, splits that cannot be allowed to grow wider. House Speaker Casper R. Taylor Jr.'s call for a One Maryland approach offers a useful framework for thinking about this issue.

So, even as Mr. Ehrlich wrestles with the most vexing and concrete problems, he must also be a healer and summoner of the best in us. In short, the new governor will be required to lead starting today.