这对我有用：

如果我正确理解你的问题，那么我认为实现这一点的最简单方法是：
注意使用whereraw而不是where，这样我们就可以使用直接的mysql代码

Logbook::whereHas('LogbookEntries', function($q) {
    $q->whereraw('date_format(date(end_date),"%Y-%m-%d") = date_format(date(start_date),"%Y-%m-%d") + interval 1 day')
})

我在我的系统上测试了一下，效果不错。但是，我的时间戳的格式是y-m-d hh:mm:ii，所以我需要date\格式来更改它们。你可能不需要这个。因此，您可能还需要尝试以下操作：

Logbook::whereHas('LogbookEntries', function($q) {
    $q->whereraw('date(end_date) = date(start_date) + interval 1 day')
})

因为这样会更整洁。
基本上，我们所做的是得到结束日期与开始日期+1天相同的条目。你离得很近，只是不太近。
我的系统，以便您可以看到它的工作：

没有whereraw语句：

>>> Task::Select('start_date','end_date')->get();
=> Illuminate\Database\Eloquent\Collection {#3325
     all: [
       App\Task {#3307
         start_date: "2018-12-20 08:00:00",
         end_date: null,
       },
       App\Task {#3291
         start_date: "2018-12-18 00:00:00",
         end_date: "2018-12-19 00:00:00",
       },
       App\Task {#3318
         start_date: "2018-12-19 00:00:00",
         end_date: "2019-01-03 00:00:00",
       },
       App\Task {#3319
         start_date: "2018-12-20 00:00:00",
         end_date: "2018-12-21 00:00:00",
       },
       App\Task {#3310
         start_date: "2018-12-20 00:00:00",
         end_date: "2018-12-21 00:00:00",
       },
       App\Task {#3317
         start_date: "2018-12-20 14:43:16",
         end_date: "2018-12-21 14:43:16",
       },
       App\Task {#3316
         start_date: "2018-12-20 14:45:27",
         end_date: "2018-12-27 14:45:27",
       },
       App\Task {#3315
         start_date: "2018-12-20 14:46:48",
         end_date: "2018-12-24 14:46:48",
       },
       App\Task {#3313
         start_date: "2018-12-21 09:25:24",
         end_date: "2018-12-24 09:25:24",
       },
       App\Task {#3298
         start_date: "2019-01-02 08:10:19",
         end_date: "2019-01-16 08:10:19",
       },
     ],
   }

用whereraw语句：

>>> Task::Select('start_date','end_date')->whereraw('date_format(date(end_date),"%Y-%m-%d") = date_format(date(start_dat
e),"%Y-%m-%d") + interval 1 day')->get();
=> Illuminate\Database\Eloquent\Collection {#3314
     all: [
       App\Task {#3312
         start_date: "2018-12-18 00:00:00",
         end_date: "2018-12-19 00:00:00",
       },
       App\Task {#3309
         start_date: "2018-12-20 00:00:00",
         end_date: "2018-12-21 00:00:00",
       },
       App\Task {#3320
         start_date: "2018-12-20 00:00:00",
         end_date: "2018-12-21 00:00:00",
       },
       App\Task {#3329
         start_date: "2018-12-20 14:43:16",
         end_date: "2018-12-21 14:43:16",
       },
     ],
   }