In this situation, the CEO is dealing with a significant interpersonal conflict between two key executives, which is affecting the overall dynamics of the organization. To address this problem effectively, the CEO needs to adopt a specific management style that facilitates resolution and promotes a healthier work environment. Here are the steps and considerations for choosing the appropriate management style:

1. Assess the Conflict: The CEO should first understand the root causes of the conflict between the head of sales and the other executive. This may involve one-on-one discussions to gather insights and perspectives from both parties.
2. Encourage Open Communication: A collaborative management style is essential in this scenario. The CEO should create a safe space for both executives to express their concerns and viewpoints without fear of repercussions. This can help in reducing tension and fostering understanding.
3. Facilitate Mediation: The CEO might consider acting as a mediator or bringing in a neutral third party to help facilitate a constructive dialogue between the conflicting parties. This can help in clarifying misunderstandings and finding common ground.
4. Focus on Team Collaboration: Emphasizing teamwork and collaboration can shift the focus from individual conflicts to shared goals. The CEO should encourage both executives to work together on a project or initiative that requires their combined expertise.
5. Implement Conflict Resolution Training: Providing training for all employees, including executives, on conflict resolution can equip them with the skills needed to address disagreements more constructively in the future.
6. Establish Clear Expectations: The CEO should outline expectations regarding professional behavior and collaboration within the organization. This can help prevent future conflicts and ensure that all team members are aligned with the company’s values.
7. Monitor Progress: After implementing these strategies, the CEO should regularly check in with both executives and their teams to monitor the situation. This demonstrates commitment to resolving the conflict and helps in making necessary adjustments if needed.

In conclusion, a collaborative and participative management style is necessary for the CEO to effectively address the conflict between the two executives. By fostering open communication, encouraging teamwork, and implementing conflict resolution strategies, the CEO can help restore harmony within the organization.