Teacher Recruitment and Retention Act of 2003 - Amends the Higher Education Act of 1965 to provide for additional amounts of student loan forgiveness for certain eligible teachers of: (1) mathematics or science in secondary schools; and (2) special education or reading in elementary and secondary schools. Requires such teachers to be highly qualified and to agree to teach for five consecutive years in schools with high enrollments of students from low-income families. (Sec. 2) Increases to $17,500 the maximum amount of loan forgiveness for such teachers under the Federal Family Education Loan and the Federal Direct Student Loan programs (with the current maximum of $5,000 continuing to apply to teachers of other subjects). Directs the Secretary of Education to pay certain portions of such loan forgiveness at specified stages of their service in the case of those eligible for the increased amount. Requires those qualifying for an increased repayment to teach at a school eligible for assistance under title I of the Elementary and Secondary Education Act of 1965 (ESEA title I school) with at least a 40 percent enrollment of students from low-income families (with the current repayment maximum continuing to apply in the case of those who teach at ESEA title I schools with at least a 30 percent enrollment of such students). (Sec. 3) Requires all teachers eligible for student loan forgiveness to be highly qualified, in keeping with requirements under ESEA. Exempts from this requirement teachers who have already begun their teaching service obligation under the current loan forgiveness program. States that such exemption shall not apply for purposes of obtaining increased loan amounts. (Sec. 4) Directs the Secretary to notify local educational agencies eligible to participate in the ESEA's Small Rural Achievement Program of the increased amounts of student loan forgiveness made available to certain teachers by this Act, and to encourage such agencies to notify their teachers of such benefits.