Born in West Penn Township, near Tamaqua, in Schuylkill County, Pennsylvania, to David and Elisabeth (Henrich) Zehner on October 11, 1805. Solomon was born on the homestead of his paternal grandfather, Adam Zehner, a German immigrant and Revolutionary War patriot. He grew up among a German speaking community, was educated to read and write in the Lutheran church, and, like his parents and grandparents, primarily spoke German throughout his life. His father, David, took over the operation of Adam's gristmill when his eyesight began to fail, and Solomon and all of his brothers followed their father into the milling profession.

Married Saloma Hoppes of the same township on April 5, 1829. Solomon and Saloma grew up attending Zion Stone Lutheran Church, which sat on land donated by Saloma's paternal grandfather, Michael, and all their children would be baptized in the Lutheran faith. Together they would have nine children:
1. David (b. June 15, 1830 near Tamaqua, Pennsylvania)
2. William (b. December 9, 1831 near Tamaqua, Pennsylvania)
3. Michael Benjamin (b. December 7, 1833 near Catawissa, Pennsylvania)
4. Elizabeth (b. December 5, 1835 near Catawissa, Pennsylvania)
5. John (b. November 18, 1837 near Catawissa, Pennsylvania)
6. Abraham (b. December 5, 1839 near Catawissa, Pennsylvania)
7. Catharine (b. February 11, 1843 near Hagerstown, Indiana)
8. Solomon (b. December 7, 1845 near Hagerstown, Indiana)
9. Gideon (b. October 26, 1847 near Hagerstown, Indiana)

Initially, Solomon and Saloma would live with his parents and youngest brothers, Gideon and Benjamin, while assisting his father in running his mill near Tamaqua. In 1832 after the birth of his first two sons, Solomon and his family moved to a farm in Catawissa Township in Columbia County, where Solomon would run his own mill. In 1842, the young family would make an arduous journey on foot to Wayne County, Indiana. Gideon had set up a prosperous milling operation in East Germantown near Cambridge City, and Solomon would settle in Jefferson Township, near Hagerstown to set up his own mill. Benjamin would later join in partnership with Solomon for four years, after having married Saloma's sister, Hester, back in Pennsylvania and living for a time in Ohio. Vandals destroyed the dam behind the mill in 1847, forcing the brothers to abandon their venture. Solomon went to work for other millers in the vicinity while his sons worked as farm hands to support the family.

After a few years of saving money, Solomon purchased some timberland near the Tippecanoe River in Marshall County, and the family would relocate there in August of 1851, again making the arduous journey on foot through the frontier wilderness. The family quickly got to work clearing the land and building a log cabin to survive through the winter. In February, a foreclosed mill and adjoining house on Wolf Creek went up for sheriff's sale. Solomon and his three oldest sons attended the sale. Solomon, unable to speak English, but with William acting as interpreter, outbid several businessmen from Plymouth in the initial round of bidding. Thinking Solomon would be unable to pay, they bowed out when the total reached $2,000, whereupon the sheriff asked for a down payment. Michael was sent to fetch David and Solomon's horse, who were standing a good distance thence, out of sight. Solomon produced his saddlebags, where he had previously sewn in gold coins, enough for a down payment. Happily the family moved into their new, finished house and set to work improving the mill and returning it to operation.

Sadly, that August Solomon would contract malaria. A passing doctor was summoned for aid, but the medicine he gave him caused him to slip into a coma from which he would not awake. He died on August 31 and was buried in nearby Pisgah Cemetery. David was the only child of age, and became the administrator of his estate, while William became a surrogate father for the remaining children. Michael would eventually take over the operation of the Wolf Creek mill.