SQL Server 2012

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CREATE TABLE table1
             (timestamp datetime,
              email varchar(256),
              transaction_id integer);
CREATE TABLE table2
             (email varchar(256),
              note varchar(MAX),
              timestamp datetime);
INSERT INTO table1
            VALUES
('2019-01-01 03:59:00', 'aa@email.com', 123),
('2018-12-31 09:00:00', 'zz@email.com', 456);
2 rows affected

INSERT INTO table2
            VALUES
('aa@email.com', 'note 1', '2019-01-01 04:00:00'),
('aa@email.com', 'note 2', '2019-01-01 04:15:00'),
('aa@email.com', 'note 3', '2019-01-01 04:20:00'),
('aa@email.com', 'note 4', '2019-01-01 04:25:00'),
('aa@email.com', 'note 5', '2019-01-01 06:15:00'),
('zz@email.com', 'note 1', '2019-01-01 08:15:00'),
('zz@email.com', 'note 2', '2019-01-01 08:16:00');
7 rows affected

SELECT *
       FROM table1 t1
            CROSS APPLY (SELECT *,
                                row_number() OVER (ORDER BY timestamp) rn
                                FROM table2 t2
                                     WHERE t2.email = t1.email
                                           AND t2.timestamp >= t1.timestamp
                                           AND t2.timestamp <= dateadd(minute, 20, t1.timestamp)) x
       WHERE x.rn = 1;


timestamp
email
transaction_id
email
note
timestamp
rn


01/01/2019 03:59:00
aa@email.com
123
aa@email.com
note 1
01/01/2019 04:00:00
1