The following 2018 fall stats are from the ASEE site. I have picked out the most common schools talked about on CC.
They are listed in the order of admission rate into engineering.
Note: Stanford, Harvard and U Florida did not provide complete stats.
Column Definitions:
School - university name
Admit rate - admission rate
SAT Avg - SAT average for engineering
Dif - difficulty of admission compared to other schools listed (1 being most difficult). This is based on SAT scores and admit rate.
eng ugrad - number of enrolled ugrad engineering students (not including CS).
eng applicants - number of applications for engineering received.
<h1>school    admit rate    sat avg    dif admit rank    #eng ugrad    #eng applicants</h1>
Harvard    4.5    1515    2    580    unk
Stanford University     5.1    1475    7    2702    unk
Columbia University    5.9    1510    4    1235    9465
Princeton University    5.9    1450    10    1059    8102
Yale    6.4    1505    7    279    6959
California Institute of Technology    6.6    1545    1    218    8208
Massachusetts Institute of Technology    6.7    1535    3    1253    21706
University of Pennsylvania    7.2    1525    4    1424    10710
Northwestern University    7.7    1445    16    1475    10433
Duke University    7.9    1535    4    866    8938
Dartmouth College    8    1490    14    387    3300
Brown University    8    1485    15    503    3176
Cornell University    9.5    1445    18    2920    13225
Carnegie Mellon University    10.9    1510    10    977    10374
University of California, Berkeley    11    1455    17    2638    25204
The Johns Hopkins University    11.5    1520    9    1448    9371
University of California, Los Angeles    11.5    1515    10    3040    26000
University of Southern California    11.5    1445    20    2124    13284
Harvey Mudd College    14.5    1525    10    577    4101
Georgia Institute of Technology    18    1460    19    6170    27250
University of Michigan    18.9    1423.75    24    4829    17659
University of California, San Diego    21.4    1310    40    4350    23388
California Polytechnic State University, San Luis Obispo    23.5    1400    26    5499    19624
Lehigh University    24.3    1395    27    1699    6041
The University of Texas at Austin    25.7    1450    22    4215    14513
Northeastern University    26.9    1475    21    2099    10273
The Pennsylvania State University    26.9    1195    51    7577    4698
Case Western Reserve University    29.3    1420    25    1251    unk
University of Virginia    30    1455    23    1694    6697
University of California, Davis    32.6    1320    45    2546    18718
University of Minnesota -Twin Cities    33.2    1360    36    3334    14457
NYU Tandon School of Engineering     33.3    1405    29    1434    6861
University of Florida    36.6    1395    31    5392    unk
Baylor University    38.4    1310    50    644    3881
University of Maryland, College Park    40    1440    27    1628    5834
Stevens Institute of Technology    41.9    1405    30    2126    6663
Stony Brook University    43    1390    36    2537    8752
University of Colorado Boulder     43    1375    39    2076    8970
The Ohio State University    43.1    1395    33    5953    10563
Worcester Polytechnic Institute    43.4    1375    40    2376    7168
University of Illinois at Urbana-Champaign    44.3    1345    49    7184    15016
North Carolina State University    48.4    1395    36    5303    8552
Rensselaer Polytechnic Institute    48.6    1430    31    2605    9751
Colorado School of Mines    49.2    1370    45    4165    12661
Purdue University    51.7    1405    34    7248    18901
University of Wisconsin-Madison    52.5    1415    34    2976    7363
Virginia Polytechnic Institute and State University    53    1370    48    6902    9758
University of Central Florida    55    1350    52    5836    8100
University of Georgia    55.5    1344    53    2007    2723
Rochester Institute of Technology    57.9    1340    56    2522    6138
Illinois Institute of Technology    60.2    1253.75    59    0    2296
University of Pittsburgh    60.5    1395    45    2521    4711
University of Washington in Seattle    61    1400    44    4163    11275
Rutgers    62.5    1420    40    3043    9442
Clemson University    65.5    1355    55    4621    6709
Rose-Hulman Institute of Technology    68.2    1365    53    1598    4471
The University of Alabama    68.5    1350    57    4569    4813
Arizona State University    72    1295    61    8231    8925
The University of Texas at Dallas    74.6    1350    58    2757    5128
University of South Carolina    76    1062.5    69    2550    3792
Michigan State University    77.8    1270    64    4571    6054
Louisiana State University    78.1    1240    66    4398    4034
Drexel University    79.7    1325    60    2544    8357
University of Arizona    80.2    1320    62    2159    2400
University of Arkansas    81    1232.5    70    2821    2649
Auburn University    82.6    1285    67    4347    4134
Texas A&M University    85    1335    62    11143    10519
University of Oklahoma    85.4    1305    67    2864    2917
The University of Alabama in Huntsville    87.1    1232.5    71    1692    1755
Iowa State University    95.9    1168.75    72    6725    5329
University of Tennessee, Knoxville    97.5    1508.75    40    2882    2572
University of Houston     97.8    1335    65    1429    1858